The graphs of f (x) = x3 + x2 – 6x and g(x) = ex + 2 – 1 have which of the following features in common?
Rational function f of x increases from the left in quadrant 3 passing through the point negative 2 comma 0 and going to a local maximum and then decreasing through the point 0 comma 0 to a local minimum and then increasing through the point 3 comma 0 to the right and the exponential function g of x increases from the left in quadrant 3 asymptotic to the line y equals negative 1 and passes through the points negative 2 comma 0 and increases through the point 0 comma 6 to the right
x-intercept
y-intercept
End behavior
Range
Answers
The end behavior of the graphs of the functions f(x) and g(x) are common.
Consider the two functions,
f(x) = x³ + x² - 6x and g(x) = [tex]e^{x+2}[/tex] - 1
Now,
y = x³ + x² - 6x
The x-intercept will be:
0 = x³ + x² - 6x
x( x² + x - 6 ) = 0
x( x - 2 )( x + 3 ) = 0
So, x = 0, 2, - 3
Hence, the x-intercepts are ( 0, 0 ), ( 2, 0 ), and ( - 3, 0 ).
The y-intercept will be:
y = x³ + x² - 6x
y = (0)³ + (0)² - 6(0)
y = 0
Hence, the y-intercept is ( 0, 0 ).
The range of the function f(x) = x³ + x² - 6x is ( - ∞, ∞ ).
Using the degree 3 and the leading coefficient 1 of the function f(x) the end behavior of the function will be:
Falls to the left and rises to the right.
For the function,
y = g(x) = [tex]e^{x+2}[/tex] - 1
The x-intercept will be:
y = [tex]e^{x+2}[/tex] - 1
0 = [tex]e^{x+2}[/tex] - 1
[tex]e^{x+2}[/tex] = 1
[tex]e^{x+2}[/tex] = e⁰
x + 2 = 0
x = - 2
Hence, the x intercept is ( - 2, 0 ).
The y-intercept will be:
y = g(x) = [tex]e^{x+2}[/tex] - 1
y = e² - 1
Hence, the y-intercept will be ( 0, e² - 1 ).
The range of the function g(x) is ( - 1, ∞ ).
The end behavior of the function g(x) constantly rises to the right in the positive y-axis.
Hence, the functions f(x) and g(x) have the end behavior in common.
Learn more about functions here:
brainly.com/question/11624077
#SPJ1
Related Questions
0.06 is 10 times Blank
Answers
Answer:
0.006
Step-by-step explanation:
Multiply 0.006 by 10.
0.006 x 10 = 0.06
Answer = 0.006
Hope this helps!
Btw, could I get Brainliest? Thanks!
Tommy earned $3,600 last summer helping his buddy at the beach club. He spent $1,860 dollars on a new computer. About what percent of his summer earnings did Tommy spend on his computer?
Answers
What type of triangle has side lengths of 2 in, 5in, and 6in?
Answers
This is Scalene triangle which has side lengths of 2 in, 5in, and 6 inches.
On the basis of the length of the sides, triangles are divided into 3 types.
What is Equilateral Triangle?
Equilateral triangle is defined as the type of triangle having all the sides equal.
What is the Isosceles Triangle?
Isosceles triangle is defined as the type of triangle having any two sides equal and one unequal.
What is the Scalene Triangle?
Scalene triangle is defined as a type of triangle having all the three sides unequal.
Thus from the above conclusion we can say that this is a Scalene triangle as all the three sides are of different lengths
i.e. 2 inches, 5 inches and 6 inches.
Learn more about types of triangles here:
https://brainly.com/question/24265179
#SPJ10
PLEASE HELP!!!!!
The graph shows the distance of a car traveling along a straight road for 8 hours. A positive velocity is motion to the right, and a negative velocity is motion to the left.
11. Determine the rates of change in distance with respect to time.
12. Between what two times is the car not moving
13. Between what two times is the car traveling to the right?
13. Between what two times is the car traveling to the left?
13. Between what two times is the car traveling the fastest?
What does the x-intercept (8, 0) represent in this situation
Answers
The graph of the distance traveled by the car to the time taken during the 8 hours along the straight road gives;
11. The rates of change between the following times, t, are;
t = 0 and t = 2 the rate of change is 30 mpht = 2 and t = 3 the rate of change is 60 mpht = 3 and t = 4 the rate of change is 0 mpht = 4 and t = 8 the rate of change is -30 mph12. The car is not moving between times 3 and 4 hours
13. The car is traveling to the right between times 0 and 3 hours
14. The car is traveling to the left between times 4 and 8 hours
15. The car is traveling fastest between times 2 and 3 hours
What is a distance–time graph?A distance–time graph is one that shows the variation of the distance traveled with respect to time, such that a positive distance traveled indicates a forward distance and a negative distance traveled indicates reversed motion.
The points on the graph in the possible question obtained online are;
(0, 0), (2, 60), (3, 120), (4, 120), (8, 0)
From the above points, the attached graph is constructed using Sheets
11. The rates of change in distance with respect to time are;
[tex] \displaystyle { \frac{ (\triangle d)_{1} }{ \triangle t} = \frac{60 - 0}{2 - 0} = 30}[/tex]; Velocity = 30 mph[tex] \displaystyle { \frac{ (\triangle d)_{2} }{\triangle t} = \frac{120 - 60}{3 - 2} = 60}[/tex]; Velocity = 60 mph[tex] \displaystyle { \frac{ (\triangle d)_{3} }{\triangle t} = \frac{120 - 1200}{4 - 3} = 0}[/tex]; Velocity = 0 mph[tex] \displaystyle { \frac{ (\triangle d)_{4} }{\triangle t} = \frac{0 - 120}{8 - 4} = - 30}[/tex]; Velocity= -30 mph12) When the car is not moving, we have that the rate of change of distance with time is zero, that is the car's distance does not change with time.
The two times between which the car is not moving is between the 3 hour and 4 hour points on the graph
13. The velocity of the car is given by the rate of change of the distance with time of the car
The positive rate of change on the graph is given between the times 0 and 3 hours after the car starts motion.
The car is traveling to the right between times, t = 0 and t = 3
14. The car has negative rate of change and therefore, negative velocity, and therefore also the car is moving to the left between times, t = 4 hours, and t = 8 hours
15. The car is traveling fastest when the rate of change of the car's distance traveled with time is highest, which is given by the times between t = 2 hours and t = 3 hours in which the car is traveling at 60 miles per hour
Learn more about distance time graph here;
https://brainly.com/question/13877898
#SPJ1
its functions ill give uu crown
Answers
The correct graphs of the puzzles/problems are
1 - B
2 - A
3 - E
4 - D
5 - C
The correct code is BAEDC.
Graphical Representation in Mathematics
It helps to study the relationship between two variables where it helps to measure the change in the variable amount with respect to another variable within a given interval of time. It helps to study the series distribution and frequency distribution for a given problem.
The correct graphs of the puzzles/problems are
1 - B
2 - A
3 - E
4 - D
5 - C
Therefore the correct code is BAEDC.
To learn more about graphic representation visit:
brainly.com/question/12658990
#SPJ1
1. Find the value of X
2. Find the measure of RSM
3. Find the measure of PTU
4. List all the angles congruent to RSM
5. List all angles congruent to PTU
Answers
The value of X is 13 .
the measure of RSM is 99°.
the measure of PTU is 99 °.
The angles congruent to∠ RSM are ∠STP , ∠OTU and ∠NST.
The angles congruent to ∠PTU are ∠STQ , ∠RSN and ∠MST.
What are the properties of parallel lines?When two lines do not cross at any point in a plane, they are said to be parallel. A pair of lines that never cross paths and do not have a common junction point are said to be parallel. Parallel lines are represented by the symbol "||".
Any two parallel lines can be separated by a consistent amount of perpendicular space.
Lines that run parallel to one another do not intersect. Parallel lines intersect at infinity is another way of putting it.
Pairs of angles are created when a transversal connects two parallel lines, for example:
Corresponding anglesAlternate interior anglesAlternate exterior anglesVertically opposite anglesLinear pairTwo lines are said to cross at a point in a plane when they do so, which is referred to as an intersection of lines.
To know more about properties of parallel lines ,visit:
brainly.com/question/28646177
#SPJ13
What is the y-intercept of =−3−7xy
Answers
The y-intercept is (0, -3)
The y-intercept is the point where the line on the graph cuts the y-axis.
To find the y-intercept, we let x equal to zero and solve for y.
y = -3 - 7x (given equation)
Substitute x = 0 in the equation,
y = -3 - 7(0)
y = -3 - 0
y = -3
Thus we can conclude that the y-intercept for the given equation y = -3 - 7x is (0, -3).
To learn more about y-intercept
visit; https://brainly.com/question/14180189
#SPJ1
The midpoint of \overline{\text{AB}}
AB
is M(2, 0)M(2,0). If the coordinates of AA are (7, -2)(7,−2), what are the coordinates of BB?
Answers
Coordinates of Point B is (-3 , 1)
To find Coordinates :
M is midpoint of AB
Coordinates of A is (7,-2)
Coordinates of M is (2,0)
Let the coordinates of B are (x,y)
To find coordinates of B :
[tex]\frac{x + 7}{2} = 2[/tex] [tex]\frac{y + (-2)}{2}= 0[/tex]
x + 7 = 4 y+ (-1) = 0
x = - 3 y = 1
coordinates of B is (-3 , 1)
Definition of coordinate :
Coordinates are two numbers or sometimes a letter and a number, that locate a specific point on a grid, known as a coordinate plane. A coordinate plane has four quadrants and two axes: the x axis (horizontal) and y axis (vertical).To learn more about Coordinates refer :
brainly.com/question/20935031
#SPJ9
3: Find the slope:
(2, 18), (4, 28)
Answers
Answer:
5
Step-by-step explanation:
Slope = (y2 - y1) / (x2 - x1)
Slope = (28 - 18) / (4 - 2)
Slope = 10 / 2 = 5
Answer:
5
Step-by-step explanation:
5 is your answer because if you plot these on a graph you would know how many points there are in between them and there are 5
i hope this helps :)
50% of the insects are ants and 50% orbitals if there are 19 ants how many insects are there
Answers
There are a total of 38 insects.
It is given that 50% of the insects are ants.It is said that 50% of the insects are beetles.There are 19 ants out of the total insects.Let the total number of the insects be "x".The percentage of both the insects is given.Also, the exact number of one of the insects is given.From the above data, we can easily form an equation in terms of percent and the exact number of insects.We know that 50% of all the insects are ants.50% of "x" is 19.0.5*x = 19x = 38Hence, the total number of insects is 38.To learn more about percentage, visit :
https://brainly.com/question/13450942
#SPJ1
. Estimate: 186,231 + 88,941
Answers
To estimate the sum, we need to round the decimals as:
186,231 ≈ 186
88,941 ≈ 89
So, we sum 186 and 89 as:
186 + 89 = 275
Therefore, the estimated sum of 186,231 + 88,941 is 275
Answer: 275
275,000
DUE TODAY ASAP!! Megan has $50 and saves $5.50 each week. Connor has $18.50 and saves $7.75 each week. After how many weeks will Megan and Connor have saved the same amount?
Answers
In 14 weeks they both will have saved the same amount if Megan has $50 and saves $5.50 each week. Connor has $18.50 and saves $7.75 each week.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Let x be the number of weeks on which Megan and Connor have saved the same amount.
Total amount(Megan) = 50 + 5.50x
Total amount(Connor) = 18.50 + 7.75x
Equate both equations:
50 + 5.50x = 18.50 + 7.75x
2.25x = 31.5
x = 14
Thus, in 14 weeks they both will have saved the same amount if Megan has $50 and saves $5.50 each week. Connor has $18.50 and saves $7.75 each week.
Learn more about the linear equation here:
brainly.com/question/11897796
#SPJ1
Question
34. Several students from Southbend Middle School are visiting the Smithsonian American Art Museum. Mrs. Mabika divided the students into 5 equal groups. There are 3 boys and 4 girls in each group. Fill in the missing numbers to find the total number of students.
Formula
__×(__+4)=__
Answers
The missing numbers to find the total number of students are 5 and 3. The equation that represents the total number of students is 5×(3+4)=35.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that Mrs. Mabika divided the students into 5 equal groups. and there are 3 boys and 4 girls in each group.
We have to find the total number of students by filling in the missing number from the given data as,
⇒5×(3+4)=35
We will add the number first in the brackets, the sum of the numbers is 7, and multiply the obtained number by 5 we get 35 as the total number of students.
Thus, the missing numbers to find the total number of students are 5 and 3. The equation that represents the total number of students is 5×(3+4)=35.
Learn more about the arithmetic operation here:
brainly.com/question/20595275
#SPJ1
Which statement describes the basis for the proof that vertical angles are congruent?
Answers
The basis for the proof vertical angles are congruent is " two angles that are each supplementary to a third angle are congruent".
Vertical angles are a pair of non-adjacent angles formed by the intersection of two straight lines.
In the provided figure.
∠1 + ∠2 = 180 degrees ( linear pair of angles)...(i)
∠ 1 + ∠4 = 180 degrees ( linear pair of angles)...(ii)
According to transitive property, if a = b and b = c then a = c
Therefore,
∠1 + ∠2 = ∠1 + ∠4...(iii)
⇒∠2 = ∠4
Similarly, we can prove that
∠1 = ∠3
Therefore, we conclude that vertically opposite angles are always equal.
Hence, the basis for the proof vertical angles are congruent is " two angles that are each supplementary to a third angle are congruent".
Thus, statement c is correct.
Learn more about vertically opposite angles here:
brainly.com/question/18045519
#SPJ1
if a number is chosen at random from the following list, then what is the probability that it is prime? (A prime number can only be divided by 1 and itself) 2, 3, 5, 7, 11, 13, 17, 19?
Answers
The probability that the chosen number from the list of the given number is prime number is 1.
The probability of an event E is defined as,
P(E) = Total favorable outcomes/Total possible outcomes
In this case,
The sample space is 2, 3, 5, 7, 11, 13, 17, 19.
Total possible outcomes are 8.
One number is chosen at random, the chosen number has to be a prime number,
Total prime number in the sample space are 2, 3, 5, 7, 11, 13, 17, 19.
So. total favorable outcomes are 8.
So, the probability that the chosen number is prime number,
P(E) = 8/8
P(E) = 1.
So, the probability of the chosen number to be a prime number is 1.
To know more about probability, visit,
https://brainly.com/question/25688842
#SPJ1
As an airline pilot, you strive forarrivals that are as close as possible toon-time. When measuring on-timearrivals based on minutes late, do youwant a higher or lower standarddeviation?LowerHigher
Answers
The standard deviation measures how far the data are from the dataset mean. The lower the standard deviation is, the closest the data are to the mean.
In this case, the pilot strives for a mean equal to 0 (zero minutes late). Also, since the pilot needs the arrivals to be as close as possible to this mean of zero minutes late (on-time), they want the data of "minutes late" to be all close to this mean. And this is achieved with a lower standard deviation.
Therefore, they want a lower standard deviation.
HELP!!!!!ASAP!!!!! I'M ON A TIMER 30 pts. to whoever is BRANLIEST
Which statement is true for the net and the solid it will form when it is folded?
Answers
Answer: Its B Glad to help
Step-by-step explanation:
Emma rotated trapezoid LMNO 90° clockwise on the coordinate plane. If angle M is 110°
and angle O is 70°, what is the degree measurement of angle M'?
Answers
110
Step-by-step explanation:
the answer is 110 cause i don't know I just searched the answer for you you welcome
The graph of g(x) is obtained by reflecting the graph of f(x)=−3|x| over the x-axis.
Which equation describes g(x)?
A:g(x)=3|x|
B:g(x)=−|x+3|
C:g(x)=|x+3|
D:g(x)=−3|x|
Answers
The equation of the graph after it is reflected is g(x) = 3|x|
How to determine the image of the reflected graph equation?The equation of the graph is given as
f(x) = -3|x|
The transformation rule is given as
Reflection over the x-axis
The mathematical representation of this transformation rule is
(x, y) = (x, -y)
The above transformation rule means that
g(x) = -f(x)
So, we have
f(x) = -3|x|
Substitute f(x) = -3|x| in g(x) = -f(x)
g(x) = -1 * -3|x|
Evaluate
g(x) = 3|x|
Hence, the equation of the reflected graph is g(x) = 3|x|
Read more about reflection at
brainly.com/question/27224272
#SPJ1
ZA and ZB are vertical angles with mZA= x and mZB= 3x - 60. What is mZA? Enter your answer in the box. O Next
Answers
we know that
vertical angles are congruent
that means
msubstitute the given values
x=3x-60
solve for x
3x-x=60
2x=60
x=30
Find the measure of angle A
mtherefore
m
Area of triangle help
Answers
Hello,
The formula of triangle is 1/2 x b x h where b is base and h is height. We know from the diagram that base is 25 cm and height is 10 cm.
Substitute in the formula:
[tex]\displaystyle{A=\dfrac{1}{2}\cdot 25\cdot 10}\\\\\displaystyle{A=25 \cdot 5}\\\\\displaystyle{A=125 }[/tex]
Therefore, the area is 125 cm². Please let me know if you have any questions!
The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 5 to 4. If there were 2348 no votes, what was the total
number of votes?
Answers
A city's residents voted on whether to raise property taxes. The yes votes outnumbered the no votes 5 to 4. The total number of votes = 1043 if there were 2348 no votes.
What is Ratio and proportion?A ratio is an ordered pair of numbers a and b, denoted by the symbol a / b, where b does not equal zero. A proportion is an equation that sets two ratios equal to each other.
For example, if there is one boy and three girls, the ratio could be written as 1: 3. (for every one boy there are 3 girls). In the ratio, the product of means equals the product of extremes.
If the cross products of two ratios are equal, they are said to be equal. The Proportion Formula is as follows: a: b:: c: d a b = c d
Therefore,
The total number of votes = 1043
yes votes / no votes = 5/4
Means there were a total of 9 votes;
So we could say:
No votes/Total votes = 4/9
So using total of 2348 votes, we can set up a proportion:
No votes/Total votes = 4/9 = x/2348
Cross multiplying ,
9392 = 9x
∴ x = 9392/9
= 1043
To learn more about Ratio and proportion refer:
https://brainly.com/question/2914376
#SPJ13
help for points please and thanks
Answers
Complete the sentence.
35 is *blank*
times as much as 5.
Answers
Julian has 51 books in a bookcase with
2 shelves. The bottom shelf has 3 more than
twice as many books as the top shelf. How
many books are on each shelf?
Answers
There are 16 books on the shelf
How to calculate the number of books on the shelf ?Let y represent the number of books on the top shelf
The number of books on the bottom shelf = 2y + 3
The total number of books in the bookcase is 51
The number of books on each shelf can be calculated as follows
y + (2y+3)= 51
y +2y +3= 51
collect the like terms
3y + 3= 51
3y= 51-3
3y= 48
divide by the coefficient of y which is 3
y= 48/3
y= 16
Hence there are 16 books on each shelf
Read more books here
https://brainly.com/question/14675376
#SPJ1
EASY POINTS:
this has become a very popular question so i'm re posting it and whoever can solve it first gets 50 points (or higher)
part 1: explain what reflections are in your own words
part 2: solve - p'(5, -4) for the glide reflection where the translation is (x,y) -> (x - 2, y - 3) and the line of reflection is y = -x
Answers
Part 1:
Reflection is a type of transformation that flips a shape in a mirror line (also called a line of reflection) so that each point is the same distance from the mirror line as its reflected point. E.g. Triangle P has been reflected in the line x = 4 x=4 x=4 to give Triangle Q.
Part 2:
1,10) is the glide reflection of point A(-5,-4).
pls help me anwser the following question will mark brainliest
Answers
The slope of the line is related to A, B and C by relation; -(A/B).
What is termed as the equation of line?A line's equation can be formed using the slope of that line and a point just on line. The slope of a line is its inclination with respect to the positive x-axis, and it is conveyed as a numeric integer, portion, or even the tangent of a angle it makes with respect to the positive x-axis. The standard form of a line equation is ax + by + c = 0. The coefficients are a and b, the variables are x and y, and the constant term is c. It is a one-degree equation with variables y and x.For the given question;
The equation of the line is given as;
5x + 2y = 10, which is written in form of Ax + By = C.
Where, A, B and C are the constant.
Write the equation in the point slope form as;
Ax + By = C
By = -Ax + C
y = -Ax/B + C/B
In which, (-A/B) is the slope of the line and C/B is the y-intercept.
Thus, the slope of the line is related to A, B and C by relation; -(A/B).
To know more about the equation of line, here
https://brainly.com/question/18831322
#SPJ13
LESSON 4 SESSION 2
Dario looks at the parallelogram and writes the expression (x + 3)(9).
a. Is Dario's expression a sum, a product, a difference, or a quotient?
Explain.
b. What are the factors of the expression (x+3)(9)? What does each factor
represent about the parallelogram?
c. What does the expression (x + 3)(9) represent? Why?
Answers
Part a: Dario's expression is product.
Part b: Factors of expression is (-3).
Part c: Expression (x + 3)(9) represent area of parallelogram.
What is meant by the term parallelogram?A parallelogram is a type of quadrilateral with opposite pairs of sides that are parallel and equal.The formula A = bh gives the area of a parallelogram, where b is the length of a base and "h" is the height.The perimeter of the a parallelogram is equal to the sum of the four side lengths. Because a parallelogram's opposite sides are equal, its perimeter can be demonstrated as 2 x a sum of adjacent sides, namely, 2 (AB + BC).For the given question;
The expression written by Dario for the parallelogram is (x + 3)(9).
Part a: Dario's expression;
The expression (x + 3)(9) is a form of multiplication or product because (x + 3) getting multiplied by (9).
Part b: Factors of expression;
For the expression (x + 3)(9), the factor are number which will make the expression zero.
(x + 3)(9) = 0
x = -3
Thus, factor is -3.
Part c: The expression (x + 3)(9) represents;
The expression (x + 3)(9) represents the area of the parallelogram as (x + 3) and (9) can be taken as the base and the height which given the area on multiplication.
To know more about parallelogram, here
https://brainly.com/question/970600
#SPJ13
Help #3 I need this by tonight
Answers
Answer:
The answer is the third option.
Step-by-step explanation:
If a₁ = 2 and aₙ = aₙ₋₁ - 4, then find the value of a4.
Answers
Answer
a₄ = -10
Explanation
If a₁ = 2 and aₙ = aₙ₋₁ - 4, then find the value of a₄.
We already know that
a₁ = 2
a₂ = a₁ - 4
a₃ = a₂ - 4
a₄ = a₃ - 4
Doing the substitutions
a₂ = a₁ - 4
a₂ = 2 - 4 = -2
a₃ = a₂ - 4
a₃ = -2 - 4 = -6
a₄ = a₃ - 4
a₄ = -6 - 4 = -10
Hope this Helps!!!
