Question 1

Use the graph of   to write an equation for the function whose graph is shown.

Accepted Answer

E

Question 2

How far will a force of 60 newtons str et

Accepted Answer

We can use Hooke's Law to solve both parts of the problem. Hooke's Law states that the force required to stretch or compress a spring is directly proportional to the displacement of the spring from its equilibrium position.

For the first part of the problem, we can use the equation:

$f = ks$

where $f$ is the force applied to the spring, $s$ is the displacement of the spring, and $k$ is the spring constant. We can solve for $s$:

$s = \frac{f}{k}$

We are given $f = 245$ N and $s = 0.25$ m. To find $k$, we can rearrange the equation:

$k = \frac{f}{s}$

Substituting in the given values, we get:

$k = \frac{245 	ext{ N}}{0.25 	ext{ m}} = 980 	ext{ N/m}$

Now we can use this value of $k$ to solve for the displacement $s$ when a force of 60 N is applied:

$s = \frac{f}{k} = \frac{60 	ext{ N}}{980 	ext{ N/m}} = 0.0612 	ext{ m} \approx 0.06 	ext{ m}$

For the second part of the problem, we are asked to find the force required to stretch the spring 0.2 m. Again, we can use Hooke's Law:

$f = ks$

We are given $s = 0.2$ m and $k = 980$ N/m. Solving for $f$, we get:

$f = ks = (980 	ext{ N/m})(0.2 	ext{ m}) = 196 	ext{ N}$

Therefore, the answer is Choice C: $0.06$ m, $196$ N.

Question 3

Select the graph of the function

Accepted Answer

The graph of the function $f ( x ) = 3 \| x \|$ will consist of two lines with slope 3, one passing through the origin and the other passing through the origin and reversed in direction in the negative x-axis. The only graph that matches this description is graph B.

Question 4

Find the inverse function of

Accepted Answer

To find the inverse function of g(x), we need to solve for x in terms of y. 
So, starting with the given function: 
y = x^7 - 4 
Adding 4 to both sides: 
y + 4 = x^7 
Taking the 7th root of both sides: 
(x + 4)^(1/7) = y^(1/7) 
Switching x and y: 
(y + 4)^(1/7) = x^(1/7) 
Which gives us: 
g^(-1)(x) = (x + 4)^(1/7) 
Therefore, the correct answer is D.

Question 5

Find the inverse function of f informally.

Accepted Answer

To find the inverse function of $f(x) = x^7$, you swap $x$ and $y$ and solve for $y$. This gives $x = y^7$, which means $y = \sqrt[7]{x}$. Therefore, the inverse function is $f^{-1}(x) = \sqrt[7]{x}$.

Question 6

Select the correct graph of the given function.

Accepted Answer

The answer of Select the correct graph of the given...

Question 7

11eb90a9_ee6c_4dd7_bccc_33f86e9ad50d_TB8855_11 11eb90a9_ee6c_4dd8_bccc_110c0a9816e4_TB8855_00

Accepted Answer

The function g(x) is a radical function with a square root, which means it is a transformation of the parent function f(x) = √x. The 3 in front of x indicates a vertical stretch by a factor of 3. Therefore, the parent function is simply f(x) = √x, and the answer is D.

Question 8

Find gof and the domain of composite function.

Accepted Answer

To find $g\circ f$, we need to first plug in $f(x)$ into $g(x)$. So we have:
$$(g\circ f)(x) = g(f(x)) = g(x^2+2) = \sqrt{x^2+2}$$
The domain of $g\circ f$ is all real numbers $x$, since the square root function can take any non-negative value as input. Therefore, the correct choice is C.

Question 9

Evaluate the function

Accepted Answer

The answer of Evaluate the function    ...

Question 10

Use the intercept form to find the equation of the line with the given intercepts. The intercept form of the equation of a line with intercepts

Accepted Answer

Given the point $(-8, 6)$ lies on the line and both intercepts are $(c, 0)$ and $(0, c)$, substituting these into the intercept form $\frac{x}{c} + \frac{y}{c} = 1$ gives $x + y = c$. Substituting the point $(-8, 6)$ into this equation gives $-8 + 6 = -2$, so $c = -2$. Thus, the equation becomes $x + y - 2 = 0$.

Question 11

Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is even and odd.

Accepted Answer

The answer of Find the coordinates of a second point...

Question 12

The suggested retail price of a new hybrid car is p dollars. The dealership advertises a factory rebate of $2000 and a 30% discount.
Write a function R in terms of p giving the cost of the hybrid car after receiving the rebate from the
Factory.

Accepted Answer

The answer of The suggested retail price of a new...

Question 13

Find the zeros of the function algebraically.

Accepted Answer

The answer of Find the zeros of the function algebraically....

Question 14

Approximate the coordinates of the points.

Accepted Answer

The answer of Approximate the coordinates of the points. ...

Question 15

Find the difference quotient and simplify your answer.

Accepted Answer

The answer of Find the difference quotient and simplify your...

Question 16

Use a graphing utility to graph the equation. Use a standard setting. Approximate any intercepts.

Accepted Answer

The answer of Use a graphing utility to graph the...

Question 17

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Accepted Answer

The answer of 11eb90a9_ee6c_74e9_bccc_d18cc17a5900_TB8855_00 11eb90a9_ee6c_74ea_bccc_d7bffaed36b2_TB8855_00...

Question 18

Show that the points form the vertices of the indicated polygon. Right triangle:

Accepted Answer

The answer of Show that the points form the vertices...

Question 19

Evaluate the function for the indicated values.

Accepted Answer

The answer of Evaluate the function for the indicated values....

Question 20

Find the x- and y-intercepts of the graph of the equation

Accepted Answer

The answer of Find the x- and y-intercepts of the...

Question 21

Select the graph of the function

Accepted Answer

The answer of Select the graph of the function ...

Question 22

Evaluate the function for the indicated values.

Accepted Answer

The answer of Evaluate the function for the indicated values....

Question 23

Use the graph of   to write an equation for the function whose graph is shown.

Accepted Answer

The answer of Use the graph of   to...

Question 24

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Accepted Answer

The answer of 11eb90a9_ee6e_97ee_bccc_6143d5c98c06_TB8855_00 11eb90a9_ee6e_beff_bccc_0d16b48e2efb_TB8855_00...

Question 25

Approximate the coordinates of the points.

Accepted Answer

The answer of Approximate the coordinates of the points. ...

Question 26

Find the zeros of the function algebraically.

Accepted Answer

The answer of Find the zeros of the function algebraically....

Question 27

Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is even and odd.

Accepted Answer

The answer of Find the coordinates of a second point...

Question 28

Find the inverse function of

Accepted Answer

The answer of Find the inverse function of  ...

Question 29

Find the x- and y-intercepts of the graph of the equation

Accepted Answer

The answer of Find the x- and y-intercepts of the...

Question 30

Find gof and the domain of composite function.

Accepted Answer

The answer of Find gof and the domain of composite...

Question 31

Find the inverse function of f informally.

Accepted Answer

The answer of Find the inverse function of f informally....

Question 32

Use a graphing utility to graph the equation. Use a standard setting. Approximate any intercepts.

Accepted Answer

The answer of Use a graphing utility to graph the...

Question 33

Find the difference quotient and simplify your answer.

Accepted Answer

The answer of Find the difference quotient and simplify your...

Question 34

Use the intercept form to find the equation of the line with the given intercepts. The intercept form of the equation of a line with intercepts

Accepted Answer

The answer of Use the intercept form to find the...

Question 35

The suggested retail price of a new hybrid car is p dollars. The dealership advertises a factory rebate of $2000 and a 30% discount.
Write a function R in terms of p giving the cost of the hybrid car after receiving the rebate from the
Factory.

Accepted Answer

The answer of The suggested retail price of a new...

Question 36

is related to the parent function. Identify the parent function   .     e. None of the above

Accepted Answer

The answer of   is related to the parent...

Question 37

Show that the points form the vertices of the indicated polygon.

Accepted Answer

The answer of Show that the points form the vertices...

Question 38

After determining whether the variation model below is of the form

Accepted Answer

The answer of After determining whether the variation model below...

Question 39

Select the correct graph of the given function.

Accepted Answer

The answer of Select the correct graph of the given...

Question 40

11eb90a9_ee6d_ad7e_bccc_855f01c72224_TB8855_00 11eb90a9_ee6d_ad7f_bccc_251831d13fce_TB8855_00

Accepted Answer

The answer of 11eb90a9_ee6d_ad7e_bccc_855f01c72224_TB8855_00 11eb90a9_ee6d_ad7f_bccc_251831d13fce_TB8855_00...

Question 41

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Accepted Answer

The answer of 11eb90a9_ee70_45c1_bccc_f508d1424f3a_TB8855_00 11eb90a9_ee70_45c2_bccc_e7e005ad5d45_TB8855_00...

Question 42

Select the correct graph of the given function.

Accepted Answer

The answer of Select the correct graph of the given...

Question 43

Write the standard form of the equation of the circle with the given characteristics.

Accepted Answer

The answer of Write the standard form of the equation...

Question 44

Evaluate the function  &#10;A) 0&#10;B) -1&#10;C) 1&#10;D) -2&#10;E) -2

Accepted Answer

The answer of Evaluate the function  &#10;A) 0&#10;B) -1&#10;C)...

Question 45

Select the graph of the given function and determine the interval(s) for which

Accepted Answer

The answer of Select the graph of the given function...

Question 46

Select the correct graph of the given function.

Accepted Answer

The answer of Select the correct graph of the given...

Question 47

Select the correct graph, showing f and g are inverse functions.

Accepted Answer

The answer of Select the correct graph, showing f and...

Question 48

Find ( f / g )(x).

Accepted Answer

The answer of Find ( f / g )(x). ...

Question 49

Select the graph of the function.

Accepted Answer

The answer of Select the graph of the function. ...

Question 50

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Accepted Answer

The answer of 11eb90a9_ee70_45be_bccc_e7eab980252d_TB8855_11 11eb90a9_ee70_45bf_bccc_9970544c491c_TB8855_00 11eb90a9_ee70_45c0_bccc_d1c8673d5d26_TB8855_00...

Question 51

The slope of line representing daily revenues y in terms of time x in years. Use the slopes to interpret any change in daily revenues for a one-day increase in time.
The line has a slope of

A) Sales decreasing 600 units/day
B) No change in sales
C) Sales increasing 600 units/day
D) None of the above

Accepted Answer

The answer of The slope of line representing daily revenues...

Question 52

Graphically estimate the x- and y-intercepts of the graph.

Accepted Answer

The answer of Graphically estimate the x- and y-intercepts of...

Question 53

Plot the points in the Cartesian plane.

Accepted Answer

The answer of Plot the points in the Cartesian plane....

Question 54

Identify the parent function and the transformation shown in the graph. Write an equation for the function shown in the graph.

Accepted Answer

The answer of Identify the parent function and the transformation...

Question 55

After determining whether the variation model below is of the form     ind the value of k.

Accepted Answer

The answer of After determining whether the variation model below...

Question 56

Find the domain of the function.

Accepted Answer

The answer of Find the domain of the function. ...

Question 57

Determine whether the function has an inverse function. If it does, find the inverse function.

Accepted Answer

The answer of Determine whether the function has an inverse...

Question 58

Find the average rate of change of the function from

Accepted Answer

The answer of Find the average rate of change of...

Question 59

How far will a force of 110 newtons s tret

Accepted Answer

The answer of     How far will...

Question 60

Show that the points form the vertices of the indicated polygon.

Accepted Answer

The answer of Show that the points form the vertices...

Question 61

Select the correct graph of the given function.

Accepted Answer

The answer of Select the correct graph of the given...

Question 62

Assume that y is directly proportional to x.   , determine a linear model that relates y and x.

Accepted Answer

The answer of Assume that y is directly proportional to...

Question 63

Determine whether the function has an inverse function. If it does, find the inverse function.

Accepted Answer

The answer of Determine whether the function has an inverse...

Question 64

The slope of line representing daily revenues y in terms of time x in years. Use the slopes to interpret any change in daily revenues for a one-day increase in time.
The line has a slope of

A) Sales decreasing 600 units/day
B) No change in sales
C) Sales increasing 600 units/day
D) None of the above