Question 1

The following is the graph of $f(x)$.
   
Sketch the graph of $f(-x)+1$.

Accepted Answer

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

Question 2

The function $f(x)$ has odd symmetry and the function $g(x)$ has even symmetry. Is the function $h(x)=f(x) * g(x)$ odd, even, or neither?

Accepted Answer

odd

Question 3

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

Accepted Answer

The answer of If the following is the graph of...

Question 4

Using the following table, find $f(2 x)$ for $x=-0.5$.

Accepted Answer

The answer of Using the following table, find $f(2 x)$...

Question 5

Which of the following describes the effect of the transformation $g(x)=\frac{f(7 x)}{7}$ on the graph of the function $f$ ?

Accepted Answer

A)  The graph is stretched vertically by a factor of 7 and stretched horizontally by a factor of 7. 
B)  The graph is stretched vertically by a factor of 7 and compressed horizontally by a factor of $\frac{1}{7}$. 
C)  The graph is compressed vertically by a factor of $\frac{1}{7}$ and stretched horizontally by a factor of 7 . 
D)  The graph is compressed vertically by a factor of $\frac{1}{7}$ and compressed horizontally by a factor of $\frac{1}{7}$. 
A)  The graph is stretched vertically by a factor of 7 and stretched horizontally by a factor of 7. 
B)  The graph is stretched vertically by a factor of 7 and compressed horizontally by a factor of $\frac{1}{7}$. 
C)  The graph is compressed vertically by a factor of $\frac{1}{7}$ and stretched horizontally by a factor of 7 . 
D)  The graph is compressed vertically by a factor of $\frac{1}{7}$ and compressed horizontally by a factor of $\frac{1}{7}$.

Question 6

Is the function $f(x)=x^{6}-7 x^{2}+6$ odd, even, or neither?

Accepted Answer

The answer of Is the function $f(x)=x^{6}-7 x^{2}+6$ odd, even,...

Question 7

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

Accepted Answer

A)  $ f(2 x)$ 
B)  $ f(x+2)$ 
C)  $2 f(x)$ 
D)  $ f(x-2)$ 
A)  $ f(2 x)$ 
B)  $ f(x+2)$ 
C)  $2 f(x)$ 
D)  $ f(x-2)$

Question 8

An odd function is increasing and concave down in the first quadrant. How does the function behave in the third quadrant?

Accepted Answer

A)  It is decreasing and concave up 
B)  It is increasing and concave down 
C)  It is increasing and concave up 
D)  It is decreasing and concave down 
A)  It is decreasing and concave up 
B)  It is increasing and concave down 
C)  It is increasing and concave up 
D)  It is decreasing and concave down

Question 9

If the graph of the line $y=2 x+1$ is reflected about the $x$-axis, the resulting line has the equation Y=------------------x + ------------

Accepted Answer

Part A: -2

Question 10

The domain of $f(x)$ is $-8 \leq x \leq 6$ and the range is $3 \leq y \leq 14$. If $g(x)=5 f(x-4)$, what is the domain and range of $g(x)$ ?

Accepted Answer

The answer of The domain of $f(x)$ is \(-8 \leq...

Question 11

The following table gives some values for the function $h(x)$. If $h(x)$ has even symmetry, what is $h(2)$ ?
$\begin{array}{ccccc}
x & -3 & -2 & -1 & 0 \
h(x) & 3 & -5 & 6 & 0
\end{array}$

Accepted Answer

The answer of The following table gives some values for...

Question 12

The point $(a, b)$ lies on the graph of $y=f(x)$. If the graph is reflected across the $y$-axis and compressed toward the $y$-axis by a factor of $d$ (with $d<1$ ), and then translated upward 4 units, what are the new coordinates for the point $(a, b)$ ?

Accepted Answer

A)  $(d(a+4), 4+b)$ 
B)  $(-d a+4, b+4)$ 
C)  $(d a, b+4)$ 
D)  $(-d a, b+4)$ 
A)  $(d(a+4), 4+b)$ 
B)  $(-d a+4, b+4)$ 
C)  $(d a, b+4)$ 
D)  $(-d a, b+4)$

Question 13

The graphs of $f$ and $g$ are shown below.
 
Which of the following gives a formula for $g(x)$ in terms of $f(x)$ ?

Accepted Answer

A)  $g(x)=\frac{1}{2} f(x)$ 
B)  $g(x)=2 f(x)$ 
C)  $g(x)=f(x-2)$ 
D)  $ g(x)=f(x)+2$ 
A)  $g(x)=\frac{1}{2} f(x)$ 
B)  $g(x)=2 f(x)$ 
C)  $g(x)=f(x-2)$ 
D)  $ g(x)=f(x)+2$

Question 14

Given the following table of values for $f(x)$, find $f(x+3)$ when $x=-3$. If you do not have sufficient information, enter "cannot determine".

Accepted Answer

The answer of Given the following table of values for...

Question 15

The point $(4,-2)$ lies on the graph of $f$. If the graph of $f$ is stretched vertically by a factor of 3 and compressed horizontally by a factor of $\frac{1}{5}$, what point must lie on the transformed graph?

Accepted Answer

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

Question 16

The following table gives values for $c(x)$, the cost per foot of drilling a well at a depth of $x$ feet. The prices given are for wells drilled on a certain ranch in Texas.
   
Estimate the cost of drilling a well that is 40 feet deep.

Accepted Answer

The answer of The following table gives values for $c(x)$,...

Question 17

Below is a graph of the function $f(x)$. If you were to sketch a graph of $y=-6 f(x)$, what point would the point $(0.6,-0.4)$ correspond to?

Accepted Answer

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

Question 18

The first figure is the graph of $f(x)$. Which of the other figures (a)-(f) show the graph of $f(0.5 x)$ ?

Accepted Answer

A)    
B)    
C)    
D)    
E)    
F)   
A)    
B)    
C)    
D)    
E)    
F)

Question 19

If $f(x)$ is an odd function, determine whether $g(x)=-6 f(x)$ is odd, even, or neither. State "cannot tell" if there is not enough information to determine.

Accepted Answer

The answer of If $f(x)$ is an odd function, determine...

Question 20

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 $-f(x)$

The following is the graph of $f(x)$ . Sketch the graph of $f(-x)+1$ .

The function $f(x)$ has odd symmetry and the function $g(x)$ has even symmetry. Is the function $h(x)=f(x) * g(x)$ odd, even, or neither?

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

Using the following table, find $f(2 x)$ for $x=-0.5$ .

Which of the following describes the effect of the transformation $g(x)=\frac{f(7 x)}{7}$ on the graph of the function $f$ ?

Is the function $f(x)=x^{6}-7 x^{2}+6$ odd, even, or neither?

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

An odd function is increasing and concave down in the first quadrant. How does the function behave in the third quadrant?

If the graph of the line $y=2 x+1$ is reflected about the $x$ -axis, the resulting line has the equation Y=------------------x + ------------

The domain of $f(x)$ is $-8 \leq x \leq 6$ and the range is $3 \leq y \leq 14$ . If $g(x)=5 f(x-4)$ , what is the domain and range of $g(x)$ ?

The following table gives some values for the function $h(x)$ . If $h(x)$ has even symmetry, what is $h(2)$ ? x -3 -2 -1 0 h(x) 3 -5 6 0

The point $(a, b)$ lies on the graph of $y=f(x)$ . If the graph is reflected across the $y$ -axis and compressed toward the $y$ -axis by a factor of $d$ (with $d<1$ ), and then translated upward 4 units, what are the new coordinates for the point $(a, b)$ ?

The graphs of $f$ and $g$ are shown below. Which of the following gives a formula for $g(x)$ in terms of $f(x)$ ?

Given the following table of values for $f(x)$ , find $f(x+3)$ when $x=-3$ . If you do not have sufficient information, enter "cannot determine".

The point $(4,-2)$ lies on the graph of $f$ . If the graph of $f$ is stretched vertically by a factor of 3 and compressed horizontally by a factor of $\frac{1}{5}$ , what point must lie on the transformed graph?

The following table gives values for $c(x)$ , the cost per foot of drilling a well at a depth of $x$ feet. The prices given are for wells drilled on a certain ranch in Texas. Estimate the cost of drilling a well that is 40 feet deep.

Below is a graph of the function $f(x)$ . If you were to sketch a graph of $y=-6 f(x)$ , what point would the point $(0.6,-0.4)$ correspond to?

The first figure is the graph of $f(x)$ . Which of the other figures (a)-(f) show the graph of $f(0.5 x)$ ?

If $f(x)$ is an odd function, determine whether $g(x)=-6 f(x)$ is odd, even, or neither. State "cannot tell" if there is not enough information to determine.

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

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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)+1f(-x)+1f(−x)+1 .

The function f(x)f(x)f(x) has odd symmetry and the function g(x)g(x)g(x) has even symmetry. Is the function h(x)=f(x)∗g(x)h(x)=f(x) * g(x)h(x)=f(x)∗g(x) odd, even, or neither?

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

Using the following table, find f(2x)f(2 x)f(2x) for x=−0.5x=-0.5x=−0.5 .

Which of the following describes the effect of the transformation g(x)=f(7x)7g(x)=\frac{f(7 x)}{7}g(x)=7f(7x)​ on the graph of the function fff ?

Is the function f(x)=x6−7x2+6f(x)=x^{6}-7 x^{2}+6f(x)=x6−7x2+6 odd, even, or neither?

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

An odd function is increasing and concave down in the first quadrant. How does the function behave in the third quadrant?

If the graph of the line y=2x+1y=2 x+1y=2x+1 is reflected about the xxx -axis, the resulting line has the equation Y=------------------x + ------------

The domain of f(x)f(x)f(x) is −8≤x≤6-8 \leq x \leq 6−8≤x≤6 and the range is 3≤y≤143 \leq y \leq 143≤y≤14 . If g(x)=5f(x−4)g(x)=5 f(x-4)g(x)=5f(x−4) , what is the domain and range of g(x)g(x)g(x) ?

The following table gives some values for the function h(x)h(x)h(x) . If h(x)h(x)h(x) has even symmetry, what is h(2)h(2)h(2) ? x -3 -2 -1 0 h(x) 3 -5 6 0

The point (a,b)(a, b)(a,b) lies on the graph of y=f(x)y=f(x)y=f(x) . If the graph is reflected across the yyy -axis and compressed toward the yyy -axis by a factor of ddd (with d<1d<1d<1 ), and then translated upward 4 units, what are the new coordinates for the point (a,b)(a, b)(a,b) ?

The graphs of fff and ggg are shown below. Which of the following gives a formula for g(x)g(x)g(x) in terms of f(x)f(x)f(x) ?

Given the following table of values for f(x)f(x)f(x) , find f(x+3)f(x+3)f(x+3) when x=−3x=-3x=−3 . If you do not have sufficient information, enter "cannot determine".

The point (4,−2)(4,-2)(4,−2) lies on the graph of fff . If the graph of fff is stretched vertically by a factor of 3 and compressed horizontally by a factor of 15\frac{1}{5}51​ , what point must lie on the transformed graph?

The following table gives values for c(x)c(x)c(x) , the cost per foot of drilling a well at a depth of xxx feet. The prices given are for wells drilled on a certain ranch in Texas. Estimate the cost of drilling a well that is 40 feet deep.

Below is a graph of the function f(x)f(x)f(x) . If you were to sketch a graph of y=−6f(x)y=-6 f(x)y=−6f(x) , what point would the point (0.6,−0.4)(0.6,-0.4)(0.6,−0.4) correspond to?

The first figure is the graph of f(x)f(x)f(x) . Which of the other figures (a)-(f) show the graph of f(0.5x)f(0.5 x)f(0.5x) ?

If f(x)f(x)f(x) is an odd function, determine whether g(x)=−6f(x)g(x)=-6 f(x)g(x)=−6f(x) is odd, even, or neither. State "cannot tell" if there is not enough information to determine.

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

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The following is the graph of $f(x)$ . Sketch the graph of $f(-x)+1$ .

The function $f(x)$ has odd symmetry and the function $g(x)$ has even symmetry. Is the function $h(x)=f(x) * g(x)$ odd, even, or neither?

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

Using the following table, find $f(2 x)$ for $x=-0.5$ .

Which of the following describes the effect of the transformation $g(x)=\frac{f(7 x)}{7}$ on the graph of the function $f$ ?

Is the function $f(x)=x^{6}-7 x^{2}+6$ odd, even, or neither?

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

If the graph of the line $y=2 x+1$ is reflected about the $x$ -axis, the resulting line has the equation Y=------------------x + ------------

The domain of $f(x)$ is $-8 \leq x \leq 6$ and the range is $3 \leq y \leq 14$ . If $g(x)=5 f(x-4)$ , what is the domain and range of $g(x)$ ?

The following table gives some values for the function $h(x)$ . If $h(x)$ has even symmetry, what is $h(2)$ ? x -3 -2 -1 0 h(x) 3 -5 6 0

The point $(a, b)$ lies on the graph of $y=f(x)$ . If the graph is reflected across the $y$ -axis and compressed toward the $y$ -axis by a factor of $d$ (with $d<1$ ), and then translated upward 4 units, what are the new coordinates for the point $(a, b)$ ?

The graphs of $f$ and $g$ are shown below. Which of the following gives a formula for $g(x)$ in terms of $f(x)$ ?

Given the following table of values for $f(x)$ , find $f(x+3)$ when $x=-3$ . If you do not have sufficient information, enter "cannot determine".

The point $(4,-2)$ lies on the graph of $f$ . If the graph of $f$ is stretched vertically by a factor of 3 and compressed horizontally by a factor of $\frac{1}{5}$ , what point must lie on the transformed graph?

The following table gives values for $c(x)$ , the cost per foot of drilling a well at a depth of $x$ feet. The prices given are for wells drilled on a certain ranch in Texas. Estimate the cost of drilling a well that is 40 feet deep.

Below is a graph of the function $f(x)$ . If you were to sketch a graph of $y=-6 f(x)$ , what point would the point $(0.6,-0.4)$ correspond to?

The first figure is the graph of $f(x)$ . Which of the other figures (a)-(f) show the graph of $f(0.5 x)$ ?

If $f(x)$ is an odd function, determine whether $g(x)=-6 f(x)$ is odd, even, or neither. State "cannot tell" if there is not enough information to determine.

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