Question 1

The following is the graph of $f(x)$.
   
Sketch the graph of $-f(x)-2$.

Accepted Answer

The answer of The following is the graph of $f(x)$.
...

Question 2

The graph of $f(x)$ contains the point $(1,-2)$. Which of the following points must be on the graph of $g(x)=2 f(x-11)$ ?

Accepted Answer

A)  $(12,-4)$ 
B)  $(1,-4)$ 
C)  $(-10,-4)$ 
D)  $(1,-15)$ 
A)  $(12,-4)$ 
B)  $(1,-4)$ 
C)  $(-10,-4)$ 
D)  $(1,-15)$

Question 3

A cup of coffee is initially at $150^{\circ} \mathrm{F}$, which is $80^{\circ} \mathrm{F}$ above room temperature. The difference between the coffee's temperature and the room's temperature decreases at the hourly rate of $80 \%$. Which of the following formulas gives $T(t)$, the coffee's temperature after $t$ hours have elapsed?

Accepted Answer

A)  $ T(t)=150+70(0.2)^{t}$ 
B)  $T(t)=80+70(0.2)^{t}$ 
C)  $T(t)=150+80(0.2)^{t}$ 
D)  $ T(t)=70+80(0.2)^{t}$ 
A)  $ T(t)=150+70(0.2)^{t}$ 
B)  $T(t)=80+70(0.2)^{t}$ 
C)  $T(t)=150+80(0.2)^{t}$ 
D)  $ T(t)=70+80(0.2)^{t}$

Question 4

The graph of $f(x)$ is shown in the first figure. Which of the other graphs (a)-(d) correspond to the formula $-f(x)-2$ ?

Accepted Answer

A)    
B) 
  
C) 
  
D) 
  
A)    
B) 
  
C) 
  
D)

Question 5

The point $(2,4)$ lies on the graph of the function $f$. Suppose the graph of $f$ is reflected across the $y$-axis, shifted upward 6 units, stretched vertically by a factor of 2 , compressed horizontally by a factor of 4 , and then shifted 6 units to the right. What point must lie on the transformed graph?

Accepted Answer

The answer of The point $(2,4)$ lies on the graph...

Question 6

The graph of $h(x)$ contains the point $(4,-1)$. What is the corresponding point on the graph of $y=h(-2 x)$ ?

Accepted Answer

The answer of The graph of $h(x)$ contains the point...

Question 7

Let $y=p(x)$ be defined by the following graph, and let $y_{0}=p\left(x_{0}\right)$ and $y_{1}=p\left(x_{1}\right)$.
   
Arrange the following values in order from least to greatest by placing a " 1 " next to the least, a "2" next to the next least, etc.
A. $p\left(x_{0}\right)$
B. $-p\left(x_{0}\right)$
C. $p\left(2 x_{0}\right)$

Accepted Answer

Part A: 1

Question 8

Let $f(x)=4^{x}$. Which of the following describe how the function $g(x)=4^{6(x-2)}$ transforms the graph of $f$ ?

Accepted Answer

A)  The graph of $f$ is compressed horizontally by a factor of $\frac{1}{6}$, then shifted to the right 2 units. 
B)  The graph of $f$ is shifted to the right 2 units, then compressed horizontally by a factor of $\frac{1}{6}$. 
C)  The graph of $f$ is compressed vertically by a factor of $4^{-12}$, and compressed horizontally by a factor of $\frac{1}{6}$. 
D)  The graph of $f$ is stretched vertically by a factor of 6 , and compressed horizontally by a factor of $\frac{1}{6}$. 
A)  The graph of $f$ is compressed horizontally by a factor of $\frac{1}{6}$, then shifted to the right 2 units. 
B)  The graph of $f$ is shifted to the right 2 units, then compressed horizontally by a factor of $\frac{1}{6}$. 
C)  The graph of $f$ is compressed vertically by a factor of $4^{-12}$, and compressed horizontally by a factor of $\frac{1}{6}$. 
D)  The graph of $f$ is stretched vertically by a factor of 6 , and compressed horizontally by a factor of $\frac{1}{6}$.

Question 9

Let $f(x)$ be the height of a box in inches. Find a formula for the height $g(t)$ in feet?

Accepted Answer

The answer of Let $f(x)$ be the height of a...

Question 10

The graph of $f(x)$ contains the point $(1,-3)$. What point must lie on the reflected graph if the graph is reflected about the $x$-axis?

Accepted Answer

The answer of The graph of $f(x)$ contains the point...

Question 11

Let $g(x)=\frac{1}{x^{2}}$. Let $h(x)$ be the function that transforms the graph of $g$ by shifting it 5 units to the right, reflecting it about the $x$-axis, and then shifting it up 7 units. Is $h(x)$ even, odd, or neither?

Accepted Answer

The answer of Let $g(x)=\frac{1}{x^{2}}$. Let $h(x)$ be the function...

Question 12

What is the formula for $y=m(-n)$ if $m(n)=n^{2}-n+4$ ?

Accepted Answer

A)  $y=-n^{2}-n-4$ 
B)  $y=n^{2}-n+4$ 
C)  $y=n^{2}+n+4$ 
D)  $y=-n^{2}+n-4$ 
A)  $y=-n^{2}-n-4$ 
B)  $y=n^{2}-n+4$ 
C)  $y=n^{2}+n+4$ 
D)  $y=-n^{2}+n-4$

Question 13

If the graph of $f(x)$ is:
 
Then the graph:
 
Represents:

Accepted Answer

A)  $f(-x)$ 
B)  $-f(x)$ 
C)  Neither $f(-x)$ or $-f(x)$ 
D)  Both $f(-x)$ and $-f(x)$ 
A)  $f(-x)$ 
B)  $-f(x)$ 
C)  Neither $f(-x)$ or $-f(x)$ 
D)  Both $f(-x)$ and $-f(x)$

Question 14

Which of the following functions are odd?

Accepted Answer

A)  $f(x)=2(x-5)^{3}$ 
B)  $g(x)=2 x^{3}+50$ 
C)  $h(x)=\frac{2 x^{2}}{5 x^{3}}$ 
D)  $ m(x)=|2 x|$ 
A)  $f(x)=2(x-5)^{3}$ 
B)  $g(x)=2 x^{3}+50$ 
C)  $h(x)=\frac{2 x^{2}}{5 x^{3}}$ 
D)  $ m(x)=|2 x|$

Question 15

Below is a graph of the function $f(x)$. If you were to sketch a graph of $y=-f(x+3)+2$, what point would the point $(-4,2)$ correspond to?

Accepted Answer

The answer of Below is a graph of the function...

Question 16

Suppose $f(x)$ is an even function. Determine whether $g(x)=f\left(\frac{x}{4}\right)$ is odd, even, or neither. Write "cannot tell" if there is not enough information to determine.

Accepted Answer

The answer of Suppose $f(x)$ is an even function. Determine...

Question 17

Which of the following describes the effect of the transformation $g(x)=9 f\left(\frac{x}{9}\right)$ on the graph of the function $f$ ?

Accepted Answer

A)  The graph is stretched vertically by a factor of 9 and stretched horizontally by a factor of 9. 
B)  The graph is stretched vertically by a factor of 9 and shrunk horizontally by a factor of $\frac{1}{9}$. 
C)  The graph is shrunk vertically by a factor of $\frac{1}{9}$ and stretched horizontally by a factor of 9 . 
D)  The graph is shrunk vertically by a factor of $\frac{1}{9}$ and shrunk horizontally by a factor of $\frac{1}{9}$. 
A)  The graph is stretched vertically by a factor of 9 and stretched horizontally by a factor of 9. 
B)  The graph is stretched vertically by a factor of 9 and shrunk horizontally by a factor of $\frac{1}{9}$. 
C)  The graph is shrunk vertically by a factor of $\frac{1}{9}$ and stretched horizontally by a factor of 9 . 
D)  The graph is shrunk vertically by a factor of $\frac{1}{9}$ and shrunk horizontally by a factor of $\frac{1}{9}$.

Question 18

Let $V=f(m)$ be the value of an investment $m$ months after the account was open. Write an expression that represents the value of the investment increased by $25 \%$.

Accepted Answer

The answer of Let $V=f(m)$ be the value of an...

Question 19

The graph of a function $f$ has been stretched vertically by a factor of 8 , compressed horizontally by a factor of 6 , and then shifted up 5 units and shifted 6 units to the left. The new graph is produced by a function $g$. Find a formula for $g$ in terms of $f$.

Accepted Answer

The answer of The graph of a function $f$ has...

Question 20

Given $f(x)=2^{x}+x^{2}$, the following figure shows the graphs of $f(x), f(-0.5 x)$, and $f(2 x)$. Which curve is the graph of $f(-0.5 x)$ ?

Accepted Answer

The answer of Given $f(x)=2^{x}+x^{2}$, the following figure shows the...

The following is the graph of $f(x)$ . Sketch the graph of $-f(x)-2$ .

The graph of $f(x)$ contains the point $(1,-2)$ . Which of the following points must be on the graph of $g(x)=2 f(x-11)$ ?

The graph of $f(x)$ is shown in the first figure. Which of the other graphs (a)-(d) correspond to the formula $-f(x)-2$ ?

The graph of $h(x)$ contains the point $(4,-1)$ . What is the corresponding point on the graph of $y=h(-2 x)$ ?

Let $f(x)=4^{x}$ . Which of the following describe how the function $g(x)=4^{6(x-2)}$ transforms the graph of $f$ ?

Let $f(x)$ be the height of a box in inches. Find a formula for the height $g(t)$ in feet?

The graph of $f(x)$ contains the point $(1,-3)$ . What point must lie on the reflected graph if the graph is reflected about the $x$ -axis?

Let $g(x)=\frac{1}{x^{2}}$ . Let $h(x)$ be the function that transforms the graph of $g$ by shifting it 5 units to the right, reflecting it about the $x$ -axis, and then shifting it up 7 units. Is $h(x)$ even, odd, or neither?

What is the formula for $y=m(-n)$ if $m(n)=n^{2}-n+4$ ?

If the graph of $f(x)$ is: Then the graph: Represents:

Which of the following functions are odd?

Below is a graph of the function $f(x)$ . If you were to sketch a graph of $y=-f(x+3)+2$ , what point would the point $(-4,2)$ correspond to?

Suppose $f(x)$ is an even function. Determine whether $g(x)=f\left(\frac{x}{4}\right)$ is odd, even, or neither. Write "cannot tell" if there is not enough information to determine.

Which of the following describes the effect of the transformation $g(x)=9 f\left(\frac{x}{9}\right)$ on the graph of the function $f$ ?

Let $V=f(m)$ be the value of an investment $m$ months after the account was open. Write an expression that represents the value of the investment increased by $25 \%$ .

The graph of a function $f$ has been stretched vertically by a factor of 8 , compressed horizontally by a factor of 6 , and then shifted up 5 units and shifted 6 units to the left. The new graph is produced by a function $g$ . Find a formula for $g$ in terms of $f$ .

Given $f(x)=2^{x}+x^{2}$ , the following figure shows the graphs of $f(x), f(-0.5 x)$ , and $f(2 x)$ . Which curve is the graph of $f(-0.5 x)$ ? $Given f(x)=2^{x}+x^{2} , the following figure shows the graphs of f(x), f(-0.5 x) , and f(2 x) . Which curve is the graph of f(-0.5 x) ?$

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Exam 6: Transformations of Functions and Their Graphs

The following is the graph of f(x)f(x)f(x) . Sketch the graph of −f(x)−2-f(x)-2−f(x)−2 .

The graph of f(x)f(x)f(x) contains the point (1,−2)(1,-2)(1,−2) . Which of the following points must be on the graph of g(x)=2f(x−11)g(x)=2 f(x-11)g(x)=2f(x−11) ?

The graph of f(x)f(x)f(x) is shown in the first figure. Which of the other graphs (a)-(d) correspond to the formula −f(x)−2-f(x)-2−f(x)−2 ?

The graph of h(x)h(x)h(x) contains the point (4,−1)(4,-1)(4,−1) . What is the corresponding point on the graph of y=h(−2x)y=h(-2 x)y=h(−2x) ?

Let f(x)=4xf(x)=4^{x}f(x)=4x . Which of the following describe how the function g(x)=46(x−2)g(x)=4^{6(x-2)}g(x)=46(x−2) transforms the graph of fff ?

Let f(x)f(x)f(x) be the height of a box in inches. Find a formula for the height g(t)g(t)g(t) in feet?

The graph of f(x)f(x)f(x) contains the point (1,−3)(1,-3)(1,−3) . What point must lie on the reflected graph if the graph is reflected about the xxx -axis?

Let g(x)=1x2g(x)=\frac{1}{x^{2}}g(x)=x21​ . Let h(x)h(x)h(x) be the function that transforms the graph of ggg by shifting it 5 units to the right, reflecting it about the xxx -axis, and then shifting it up 7 units. Is h(x)h(x)h(x) even, odd, or neither?

What is the formula for y=m(−n)y=m(-n)y=m(−n) if m(n)=n2−n+4m(n)=n^{2}-n+4m(n)=n2−n+4 ?

If the graph of f(x)f(x)f(x) is: Then the graph: Represents:

Which of the following functions are odd?

Below is a graph of the function f(x)f(x)f(x) . If you were to sketch a graph of y=−f(x+3)+2y=-f(x+3)+2y=−f(x+3)+2 , what point would the point (−4,2)(-4,2)(−4,2) correspond to?

Suppose f(x)f(x)f(x) is an even function. Determine whether g(x)=f(x4)g(x)=f\left(\frac{x}{4}\right)g(x)=f(4x​) is odd, even, or neither. Write "cannot tell" if there is not enough information to determine.

Which of the following describes the effect of the transformation g(x)=9f(x9)g(x)=9 f\left(\frac{x}{9}\right)g(x)=9f(9x​) on the graph of the function fff ?

Let V=f(m)V=f(m)V=f(m) be the value of an investment mmm months after the account was open. Write an expression that represents the value of the investment increased by 25%25 \%25% .

The graph of a function fff has been stretched vertically by a factor of 8 , compressed horizontally by a factor of 6 , and then shifted up 5 units and shifted 6 units to the left. The new graph is produced by a function ggg . Find a formula for ggg in terms of fff .

Given f(x)=2x+x2f(x)=2^{x}+x^{2}f(x)=2x+x2 , the following figure shows the graphs of f(x),f(−0.5x)f(x), f(-0.5 x)f(x),f(−0.5x) , and f(2x)f(2 x)f(2x) . Which curve is the graph of f(−0.5x)f(-0.5 x)f(−0.5x) ?

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The following is the graph of $f(x)$ . Sketch the graph of $-f(x)-2$ .

The graph of $f(x)$ contains the point $(1,-2)$ . Which of the following points must be on the graph of $g(x)=2 f(x-11)$ ?

The graph of $f(x)$ is shown in the first figure. Which of the other graphs (a)-(d) correspond to the formula $-f(x)-2$ ?

The graph of $h(x)$ contains the point $(4,-1)$ . What is the corresponding point on the graph of $y=h(-2 x)$ ?

Let $f(x)=4^{x}$ . Which of the following describe how the function $g(x)=4^{6(x-2)}$ transforms the graph of $f$ ?

Let $f(x)$ be the height of a box in inches. Find a formula for the height $g(t)$ in feet?

The graph of $f(x)$ contains the point $(1,-3)$ . What point must lie on the reflected graph if the graph is reflected about the $x$ -axis?

Let $g(x)=\frac{1}{x^{2}}$ . Let $h(x)$ be the function that transforms the graph of $g$ by shifting it 5 units to the right, reflecting it about the $x$ -axis, and then shifting it up 7 units. Is $h(x)$ even, odd, or neither?

What is the formula for $y=m(-n)$ if $m(n)=n^{2}-n+4$ ?

If the graph of $f(x)$ is: Then the graph: Represents:

Below is a graph of the function $f(x)$ . If you were to sketch a graph of $y=-f(x+3)+2$ , what point would the point $(-4,2)$ correspond to?

Suppose $f(x)$ is an even function. Determine whether $g(x)=f\left(\frac{x}{4}\right)$ is odd, even, or neither. Write "cannot tell" if there is not enough information to determine.

Which of the following describes the effect of the transformation $g(x)=9 f\left(\frac{x}{9}\right)$ on the graph of the function $f$ ?

Let $V=f(m)$ be the value of an investment $m$ months after the account was open. Write an expression that represents the value of the investment increased by $25 \%$ .

The graph of a function $f$ has been stretched vertically by a factor of 8 , compressed horizontally by a factor of 6 , and then shifted up 5 units and shifted 6 units to the left. The new graph is produced by a function $g$ . Find a formula for $g$ in terms of $f$ .

Given $f(x)=2^{x}+x^{2}$ , the following figure shows the graphs of $f(x), f(-0.5 x)$ , and $f(2 x)$ . Which curve is the graph of $f(-0.5 x)$ ? $Given f(x)=2^{x}+x^{2} , the following figure shows the graphs of f(x), f(-0.5 x) , and f(2 x) . Which curve is the graph of f(-0.5 x) ?$