Question 1

Use the vertical line test to determine whether or not the graph is a graph in which y is a function of x.
-

Accepted Answer

A) function 
B) not a function 
A) function 
B) not a function

Question 2

Use the given conditions to write an equation for the line in point-slope form.
-Slope $= 3$, passing through $( - 7,8 )$

Accepted Answer

A)  $y - 8 = 3 ( x + 7 )$ 
B)  $y + 8 = 3 ( x - 7 )$ 
C)  $y = 3 x + 29$ 
D)  $x - 8 = 3 ( y + 7 )$ 
A)  $y - 8 = 3 ( x + 7 )$ 
B)  $y + 8 = 3 ( x - 7 )$ 
C)  $y = 3 x + 29$ 
D)  $x - 8 = 3 ( y + 7 )$

Question 3

Determine whether the equation defines y as a function of x.
-$$x y + 9 y = 1$$

Accepted Answer

A)  $y$ is a function of $x$ 
B)  $y$ is not a function of $x$ 
A)  $y$ is a function of $x$ 
B)  $y$ is not a function of $x$

Question 4

Determine whether the relation is a function.
-{(-6, -5), (-3, -7), (4, 6), (4, 8)}

Accepted Answer

A) Not a function 
B) Function 
A) Not a function 
B) Function

Question 5

Give the domain and range of the relation.
-{(5, -4), (1, -3), (1, 0), (10, 3), (26, 5)}

Accepted Answer

A) domain: {-4, -3, 0, 3, 5}; range: {5, 10, 1, 26} 
B) domain: {5, 10, 1, 26}; range: {-4, -3, 3, 5} 
C) domain: {-4, -3, 3, 5}; range: {5, 10, 1, 26} 
D) domain: {5, 10, 1, 26}; range: {-4, -3, 0, 3, 5} 
A) domain: {-4, -3, 0, 3, 5}; range: {5, 10, 1, 26} 
B) domain: {5, 10, 1, 26}; range: {-4, -3, 3, 5} 
C) domain: {-4, -3, 3, 5}; range: {5, 10, 1, 26} 
D) domain: {5, 10, 1, 26}; range: {-4, -3, 0, 3, 5}

Question 6

Evaluate the piecewise function at the given value of the independent variable.
-$$f ( x ) = \left\{ \begin{array} { l } 
3 x - 2 \text { if } x < 1 \
2 x + 3 \quad \text { if } x \geq 1
\end{array} ; f ( 1 ) \right.$$

Accepted Answer

A)  0 
B)  5 
C)  6 
D)  3 
A)  0 
B)  5 
C)  6 
D)  3

Question 7

Identify the intercepts
-

Accepted Answer

A)  $( - 1 , - 1 ) , ( 1,1 )$ 
B)  $( 1,0 ) , ( 0,1 )$ 
C)  $( - 1,0 ) , ( 0 , - 1 )$ 
D)  $( - 1,0 ) , ( 0,1 )$ 
A)  $( - 1 , - 1 ) , ( 1,1 )$ 
B)  $( 1,0 ) , ( 0,1 )$ 
C)  $( - 1,0 ) , ( 0 , - 1 )$ 
D)  $( - 1,0 ) , ( 0,1 )$

Question 8

Use the given conditions to write an equation for the line in point-slope form.
-Passing through $( 1 , - 5 )$ with $x$-intercept $= - 1$

Accepted Answer

A)  $y - 5 = - \frac { 5 } { 2 } ( x + 1 )$ or $y = - \frac { 5 } { 2 } ( x + 1 )$ 
B)  $y + 5 = - \frac { 5 } { 2 } ( x - 1 )$ or $y = - \frac { 5 } { 2 } ( x + 1 )$ 
C)  $y + 5 = - \frac { 5 } { 2 } ( x - 1 )$ or $y = - \frac { 5 } { 2 } ( x - 1 )$ 
D)  $y - 1 = - \frac { 5 } { 2 } x$ or $y - 5 = - \frac { 5 } { 2 } ( x + 1 )$ 
A)  $y - 5 = - \frac { 5 } { 2 } ( x + 1 )$ or $y = - \frac { 5 } { 2 } ( x + 1 )$ 
B)  $y + 5 = - \frac { 5 } { 2 } ( x - 1 )$ or $y = - \frac { 5 } { 2 } ( x + 1 )$ 
C)  $y + 5 = - \frac { 5 } { 2 } ( x - 1 )$ or $y = - \frac { 5 } { 2 } ( x - 1 )$ 
D)  $y - 1 = - \frac { 5 } { 2 } x$ or $y - 5 = - \frac { 5 } { 2 } ( x + 1 )$

Question 9

Evaluate the piecewise function at the given value of the independent variable.
-$f ( x ) = \left\{ \begin{array} { l l } x - 1 & \text { if } x > - 3 \ - ( x - 1 ) & \text { if } x \leq - 3 \end{array} ; f ( - 5 ) \right.$

Accepted Answer

A)  17 
B)  $- 5$ 
C)  6 
D)  $- 6$ 
A)  17 
B)  $- 5$ 
C)  6 
D)  $- 6$

Question 10

Determine whether the relation is a function.
-{(-2, -9), (3, -5), (6, 6), (8, 1), (11, 2)}

Accepted Answer

A) Function 
B) Not a function 
A) Function 
B) Not a function

Question 11

Use the graph to determine the function's domain and range.
-

Accepted Answer

A)  domain: $x = - \frac { 5 } { 2 }$
range: $( - \infty , \infty )$ 
B)  domain: $x = - \frac { 5 } { 2 }$
range: $\mathrm { y } = 5$ 
C)  domain: $( - \infty , \infty )$
range: $y = 5$ 
D)  domain: $( - \infty , \infty )$
range: $( - \infty , \infty )$ 
A)  domain: $x = - \frac { 5 } { 2 }$
range: $( - \infty , \infty )$ 
B)  domain: $x = - \frac { 5 } { 2 }$
range: $\mathrm { y } = 5$ 
C)  domain: $( - \infty , \infty )$
range: $y = 5$ 
D)  domain: $( - \infty , \infty )$
range: $( - \infty , \infty )$

Question 12

Determine whether the relation is a function.
-{(-8, -9), (-8, 9), (1, 3), (3, 5), (10, -9)}

Accepted Answer

A) Not a function 
B) Function 
A) Not a function 
B) Function

Question 13

Determine whether the equation defines y as a function of x.
-$$x + y ^ { 2 } = 4$$

Accepted Answer

A)  $y$ is a function of $x$ 
B)  $y$ is not a function of $x$ 
A)  $y$ is a function of $x$ 
B)  $y$ is not a function of $x$

Question 14

Solve the problem.
-The total cost in dollars for a certain company to produce x empty jars to be used by a jelly producer is given by the function C(x)= 0.8x + 40,000. Find C(50,000), the cost of producing 50,000 jars.

Accepted Answer

A) $40.80 
B) $80,000 
C) $40,000 
D) $50,040 
A) $40.80 
B) $80,000 
C) $40,000 
D) $50,040

Question 15

Use the given conditions to write an equation for the line in slope-intercept form.
-Glope $= 3$, passing through $( 3,8 )$

Accepted Answer

A)  $y - 8 = 3 x - 3$ 
B)  $y = 3 x - 1$ 
C)  $y = 3 x + 1$ 
D)  $y - 8 = x - 3$ 
A)  $y - 8 = 3 x - 3$ 
B)  $y = 3 x - 1$ 
C)  $y = 3 x + 1$ 
D)  $y - 8 = x - 3$

Question 16

Find the slope of the line that goes through the given points.
-(-1, 7), (-8, 7)

Accepted Answer

A) 9 
B) 1 
C) 2 
D) 0 
A) 9 
B) 1 
C) 2 
D) 0

Question 17

Identify the intervals where the function is changing as requested.
-Decreasing

Accepted Answer

A)  $( - 3 , - 2 )$ 
B)  $( - \infty , - 3 )$ 
C)  $( - \infty , - 2 )$ 
D)  $( 0 , - 2 )$ 
A)  $( - 3 , - 2 )$ 
B)  $( - \infty , - 3 )$ 
C)  $( - \infty , - 2 )$ 
D)  $( 0 , - 2 )$

Question 18

Identify the intervals where the function is changing as requested.
-Increasing

Accepted Answer

A)  $( - 2,0 )$ 
B)  $( - 2 , \infty )$ 
C)  $( 3 , \infty )$ 
D)  $( 3,6 )$ 
A)  $( - 2,0 )$ 
B)  $( - 2 , \infty )$ 
C)  $( 3 , \infty )$ 
D)  $( 3,6 )$

Question 19

Graph the given functions on the same rectangular coordinate system. Describe how the graph of g is related to the graph
of f.
-$f(x)=2 x^{2}, g(x)=2 x^{2}-3$

Accepted Answer

A)  $g$ shifts the graph of $f$ vertically down 3 units
  
B)  $g$ shifts the graph of $f$ vertically up 3 units
  
C)  g shifts the graph of f vertically down 3 units
  
D)  g shifts the graph of f vertically up 3 units
  
A)  $g$ shifts the graph of $f$ vertically down 3 units
  
B)  $g$ shifts the graph of $f$ vertically up 3 units
  
C)  g shifts the graph of f vertically down 3 units
  
D)  g shifts the graph of f vertically up 3 units

Question 20

Use the graph to find the indicated function value.
-y = f(x). Find f(-3)

Accepted Answer

A) 0.4 
B) -1.6 
C) -0.4 
D) 1.6 
A) 0.4 
B) -1.6 
C) -0.4 
D) 1.6

Use the vertical line test to determine whether or not the graph is a graph in which y is a function of x. -

Use the given conditions to write an equation for the line in point-slope form. -Slope $= 3$ , passing through $( - 7,8 )$

Determine whether the equation defines y as a function of x. - $x y + 9 y = 1$

Determine whether the relation is a function. -{(-6, -5), (-3, -7), (4, 6), (4, 8)}

Give the domain and range of the relation. -{(5, -4), (1, -3), (1, 0), (10, 3), (26, 5)}

Evaluate the piecewise function at the given value of the independent variable. - $f ( x ) = \left\{ \begin{array} { l } 3 x - 2 \text { if } x < 1 \\2 x + 3 \quad \text { if } x \geq 1\end{array} ; f ( 1 ) \right.$

Identify the intercepts -

Use the given conditions to write an equation for the line in point-slope form. -Passing through $( 1 , - 5 )$ with $x$ -intercept $= - 1$

Evaluate the piecewise function at the given value of the independent variable. - $f ( x ) = \left\{ \begin{array} { l l } x - 1 & \text { if } x > - 3 \\ - ( x - 1 ) & \text { if } x \leq - 3 \end{array} ; f ( - 5 ) \right.$

Determine whether the relation is a function. -{(-2, -9), (3, -5), (6, 6), (8, 1), (11, 2)}

Use the graph to determine the function's domain and range. -

Determine whether the relation is a function. -{(-8, -9), (-8, 9), (1, 3), (3, 5), (10, -9)}

Determine whether the equation defines y as a function of x. - $x + y ^ { 2 } = 4$

Solve the problem. -The total cost in dollars for a certain company to produce x empty jars to be used by a jelly producer is given by the function C(x)= 0.8x + 40,000. Find C(50,000), the cost of producing 50,000 jars.

Use the given conditions to write an equation for the line in slope-intercept form. -Glope $= 3$ , passing through $( 3,8 )$

Find the slope of the line that goes through the given points. -(-1, 7), (-8, 7)

Identify the intervals where the function is changing as requested. -Decreasing

Identify the intervals where the function is changing as requested. -Increasing

Use the graph to find the indicated function value. -y = f(x). Find f(-3)

Equations and Inequalities

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Systems of Equations and Inequalities

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Exam 2: Functions and Graphs