Question 1

Determine if the graph is symmetric with respect to x-axis, y-axis, and/or the origin.
-

Accepted Answer

A)   y-a x i s 
B)  Origin 
C)   x -axis, origin 
D)   x -axis 
A)   y-a x i s 
B)  Origin 
C)   x -axis, origin 
D)   x -axis

Question 2

Determine the intervals on which the function is increasing, decreasing, and constant.
- 
A) Increasing on  (-2,0)  and  (3,4) ; Decreasing on  (-5,-2)  and  (1,3) 
B) Increasing on  (-2,0)  and  (3,5) ; Decreasing on  (1,3) ; Constant on  (-5,-2) 
C) Increasing on  (-1,0)  and  (3,5) ; Decreasing on  (0,3) ; Constant on  (-5,-3) 
D) Increasing on  (1,3) ; Decreasing on  (-2,0)  and  (3,5) ; Constant on  (2,5)

Accepted Answer

The answer of Determine the intervals on which the function...

Question 3

The given point is on the graph of y = f(x). Find a point on the graph of y = g(x).
-g(x) = f(-4x); (5, -4)

Accepted Answer

A)  $\left( - \frac { 5 } { 4 } , - 4 \right)$ 
B)  (20,4) 
C)  $\left( \frac { 1 } { 20 } , - 5 \right)$ 
D)  (-20,-4) 
A)  $\left( - \frac { 5 } { 4 } , - 4 \right)$ 
B)  (20,4) 
C)  $\left( \frac { 1 } { 20 } , - 5 \right)$ 
D)  (-20,-4)

Question 4

Find f(x) and g(x) such that h(x) = $$= ( f \circ g ) ( x )$$
-$h ( x ) = \sqrt { \frac { x + 2 } { x - 1 } }$
A) $f ( x ) = \frac { x + 2 } { x - 1 } , g ( x ) = \sqrt { x }$
B) $f ( x ) = \sqrt { \frac { 1 } { x - 1 } } , g ( x ) = x + 2$
C) $f ( x ) = \sqrt { x + 2 } , g ( x ) = \frac { 1 } { x - 1 }$
D) $f ( x ) = \sqrt { x } , g ( x ) = \frac { x + 2 } { x - 1 }$

Accepted Answer

The answer of Find f(x) and g(x) such that h(x)...

Question 5

Answer the question.
-How can the graph of $f ( x ) = 0.4 ( x + 7 ) ^ { 2 } - 9$ be obtained from the graph of $y = x ^ { 2 } ?$

Accepted Answer

A)  Shift it horizontally 7 units to the right. Shrink it vertically by a factor of  0.4 . Shift it 9 units up. 
B)  Shift it horizontally 7 units to the left. Shrink it vertically by a factor of  0.4 . Shift it 9 units down. 
C)  Shift it horizontally 7 units to the left. Shrink it horizontally by a factor of 0.4. Shift it 9 units down. 
D)  Shift it horizontally 9 units to the left. Stretch it vertically by a factor of 8 . Shift it 7 units down. 
A)  Shift it horizontally 7 units to the right. Shrink it vertically by a factor of  0.4 . Shift it 9 units up. 
B)  Shift it horizontally 7 units to the left. Shrink it vertically by a factor of  0.4 . Shift it 9 units down. 
C)  Shift it horizontally 7 units to the left. Shrink it horizontally by a factor of 0.4. Shift it 9 units down. 
D)  Shift it horizontally 9 units to the left. Stretch it vertically by a factor of 8 . Shift it 7 units down.

Question 6

Write an equation for the piecewise function.
-

Accepted Answer

A)  $f ( x ) = \left\{ \begin{array} { l l } 
4 , & \text { for } x  0
\end{array} \right.$ 
C)  $f ( x ) = \left\{ \begin{array} { l l } 
- 4 , & \text { for } x \leq 0 \
4 , & \text { for } x > 0
\end{array} \right.$ 
D)  $f ( x ) = \left\{ \begin{array} { l l } 
4 x , & \text { for } x \leq 0 \
- 4 x , & \text { for } x > 0
\end{array} \right.$ 
A)  $f ( x ) = \left\{ \begin{array} { l l } 
4 , & \text { for } x  0
\end{array} \right.$ 
C)  $f ( x ) = \left\{ \begin{array} { l l } 
- 4 , & \text { for } x \leq 0 \
4 , & \text { for } x > 0
\end{array} \right.$ 
D)  $f ( x ) = \left\{ \begin{array} { l l } 
4 x , & \text { for } x \leq 0 \
- 4 x , & \text { for } x > 0
\end{array} \right.$

Question 7

The graph of the function f is shown below. Match the function g with the correct graph.
-g(x)= -f(-x)-3

Accepted Answer

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

Question 8

Find the requested function value.
- 
Find

Accepted Answer

A)   -20 
B)    
C)  60 
D)   -2 
A)   -20 
B)    
C)  60 
D)   -2

Question 9

Determine algebraically whether the function is even, odd, or neither even nor odd.
-

Accepted Answer

A)  Even 
B)  Odd 
C)  Neither 
A)  Even 
B)  Odd 
C)  Neither

Question 10

The graph of the function f is shown below. Match the function g with the correct graph.
-g(x)= f(x+2)

Accepted Answer

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

Question 11

Graph the equation.
- 
A)   
B)  
C)  
D)

Accepted Answer

The answer of Graph the equation.
- 
A)   
B)...

Question 12

For the pair of functions, find the indicated domain.
-$f ( x ) = 2 x - 5 , g ( x ) = \sqrt { x + 10 }$
Find the domain of  f+g

Accepted Answer

A)  $[ 0 , \infty )$ 
B)   (-10,10) 
C)  $[ 10 , \infty )$ 
D)  $[ - 10 , \infty )$ 
A)  $[ 0 , \infty )$ 
B)   (-10,10) 
C)  $[ 10 , \infty )$ 
D)  $[ - 10 , \infty )$

Question 13

Solve the problem.
-The weight that a horizontal beam can support varies inversely as the length of the beam. Suppose that a  2-m  beam can support  560kg . How many kilograms can a  2-m  beam support?

Accepted Answer

A)   0.0018 kg 
B)   560 kg 
C)   0.0071 kg 
D)   140 kg 
A)   0.0018 kg 
B)   560 kg 
C)   0.0071 kg 
D)   140 kg

Question 14

Graph the function.
-

Accepted Answer

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

Question 15

Find f(x) and g(x) such that h(x) = (f g)(x).
-$h ( x ) = \left( \frac { x ^ { 3 } + 5 } { 5 - x ^ { 3 } } \right) ^ { 8 }$

Accepted Answer

A)  $f ( x ) = \left( x ^ { 3 } + 5 \right) ^ { 8 } , g ( x ) = 5 - x ^ { 3 }$ 
B)  $f ( x ) = \frac { 1 } { x ^ { 8 } } , g ( x ) = \frac { x ^ { 3 } + 5 } { 5 - x ^ { 3 } }$ 
C)  $f ( x ) = \frac { x ^ { 3 } + 5 } { 5 - x ^ { 3 } } , g ( x ) = x ^ { 8 }$ 
D)  $f ( x ) = x ^ { 8 } , g ( x ) = \frac { x ^ { 3 } + 5 } { 5 - x ^ { 3 } }$ 
A)  $f ( x ) = \left( x ^ { 3 } + 5 \right) ^ { 8 } , g ( x ) = 5 - x ^ { 3 }$ 
B)  $f ( x ) = \frac { 1 } { x ^ { 8 } } , g ( x ) = \frac { x ^ { 3 } + 5 } { 5 - x ^ { 3 } }$ 
C)  $f ( x ) = \frac { x ^ { 3 } + 5 } { 5 - x ^ { 3 } } , g ( x ) = x ^ { 8 }$ 
D)  $f ( x ) = x ^ { 8 } , g ( x ) = \frac { x ^ { 3 } + 5 } { 5 - x ^ { 3 } }$

Question 16

For the pair of functions, find the indicated sum, difference, product, or quotient.
-$f ( x ) = x ^ { 2 } - 1 , g ( x ) = 9 x + 1$
Find $( f / g ) \left( - \frac { 1 } { 9 } \right)$

Accepted Answer

A)  $\frac { 1 } { 2 }$ 
B)  0 
C)  does not exist 
D)  $- \frac { 2 } { 3 }$ 
A)  $\frac { 1 } { 2 }$ 
B)  0 
C)  does not exist 
D)  $- \frac { 2 } { 3 }$

Question 17

For the pair of functions, find the indicated domain.
-f(x)=2 x-5, $g ( x ) = \sqrt { x + 5 }$
Find the domain of $\text { g of. }$
A) $[ - \infty , 0 )$
B) $[ 5 , \infty )$
C) $[ 0 , \infty )$
D)  (-5,5)

Accepted Answer

The answer of For the pair of functions, find the...

Question 18

Write an equation for the piecewise function.
- 
A) $f ( x ) = \left\{ \begin{array} { l l } 
2 x - 3 , & \text { for } x \neq 3 \
- 3 , & \text { for } x = 3
\end{array} \right.$
B) $f ( x ) = \left\{ \begin{array} { l l } 
x - 3 , & \text { for } x \neq 3 \
- 2 , & \text { for } x = 3
\end{array} \right.$
C) $f ( x ) = \left\{ \begin{array} { l l } 
2 x - 3 , & \text { for } x \neq 3 \
- 2 , & \text { for } x = 3
\end{array} \right.$
D) $f ( x ) = \left\{ \begin{array} { l l } 
2 x - 3 , & \text { for } x < 3 \
2 x + 3 , & \text { for } x \geq 3
\end{array} \right.$

Accepted Answer

The answer of Write an equation for the piecewise function.
-...

Question 19

Determine whether the given function is even, odd, or neither even nor odd.
- 
A) Neither
B) Odd
C) Even

Accepted Answer

The answer of Determine whether the given function is even,...

Question 20

For the function f, construct and simplify the difference quotient $$\frac { f ( x + h ) - f ( x ) } { h }$$
-$f ( x ) = \frac { 1 } { 5 x }$
A) $\frac { - 1 } { x ( x + h ) }$
B) $\frac { - 1 } { 5 \times ( x + h ) }$
C) $\frac { 1 } { 5 x }$
D) 0

Accepted Answer

The answer of For the function f, construct and simplify...

Determine if the graph is symmetric with respect to x-axis, y-axis, and/or the origin. -

The given point is on the graph of y = f(x). Find a point on the graph of y = g(x). -g(x) = f(-4x); (5, -4)

Answer the question. -How can the graph of $f ( x ) = 0.4 ( x + 7 ) ^ { 2 } - 9$ be obtained from the graph of $y = x ^ { 2 } ?$

Write an equation for the piecewise function. -

The graph of the function f is shown below. Match the function g with the correct graph. -g(x)= -f(-x)-3

Find the requested function value. - Find

Determine algebraically whether the function is even, odd, or neither even nor odd. -

The graph of the function f is shown below. Match the function g with the correct graph. -g(x)= f(x+2)

Graph the equation. - A) B) C) D)

For the pair of functions, find the indicated domain. - $f ( x ) = 2 x - 5 , g ( x ) = \sqrt { x + 10 }$ Find the domain of f+g

Solve the problem. -The weight that a horizontal beam can support varies inversely as the length of the beam. Suppose that a 2-m beam can support 560kg . How many kilograms can a 2-m beam support?

Graph the function. -

Find f(x) and g(x) such that h(x) = (f g)(x). - $h ( x ) = \left( \frac { x ^ { 3 } + 5 } { 5 - x ^ { 3 } } \right) ^ { 8 }$

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = x ^ { 2 } - 1 , g ( x ) = 9 x + 1$ Find $( f / g ) \left( - \frac { 1 } { 9 } \right)$

For the pair of functions, find the indicated domain. -f(x)=2 x-5, $g ( x ) = \sqrt { x + 5 }$ Find the domain of $\text { g of. }$ A) $[ - \infty , 0 )$ B) $[ 5 , \infty )$ C) $[ 0 , \infty )$ D) (-5,5)

Determine whether the given function is even, odd, or neither even nor odd. - A) Neither B) Odd C) Even

For the function f, construct and simplify the difference quotient $\frac { f ( x + h ) - f ( x ) } { h }$ - $f ( x ) = \frac { 1 } { 5 x }$ A) $\frac { - 1 } { x ( x + h ) }$ B) $\frac { - 1 } { 5 \times ( x + h ) }$ C) $\frac { 1 } { 5 x }$ D) 0

Graphs, Functions, and Models

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Exam 2: More on Functions

Determine if the graph is symmetric with respect to x-axis, y-axis, and/or the origin. -

The given point is on the graph of y = f(x). Find a point on the graph of y = g(x). -g(x) = f(-4x); (5, -4)

Answer the question. -How can the graph of f(x)=0.4(x+7)2−9f ( x ) = 0.4 ( x + 7 ) ^ { 2 } - 9f(x)=0.4(x+7)2−9 be obtained from the graph of y=x2?y = x ^ { 2 } ?y=x2?

Write an equation for the piecewise function. -

The graph of the function f is shown below. Match the function g with the correct graph. -g(x)= -f(-x)-3

Find the requested function value. - Find

Determine algebraically whether the function is even, odd, or neither even nor odd. -

The graph of the function f is shown below. Match the function g with the correct graph. -g(x)= f(x+2)

Graph the equation. - A) B) C) D)

For the pair of functions, find the indicated domain. - f(x)=2x−5,g(x)=x+10f ( x ) = 2 x - 5 , g ( x ) = \sqrt { x + 10 }f(x)=2x−5,g(x)=x+10​ Find the domain of f+g

Solve the problem. -The weight that a horizontal beam can support varies inversely as the length of the beam. Suppose that a 2-m beam can support 560kg . How many kilograms can a 2-m beam support?

Graph the function. -

Find f(x) and g(x) such that h(x) = (f g)(x). - h(x)=(x3+55−x3)8h ( x ) = \left( \frac { x ^ { 3 } + 5 } { 5 - x ^ { 3 } } \right) ^ { 8 }h(x)=(5−x3x3+5​)8

For the pair of functions, find the indicated sum, difference, product, or quotient. - f(x)=x2−1,g(x)=9x+1f ( x ) = x ^ { 2 } - 1 , g ( x ) = 9 x + 1f(x)=x2−1,g(x)=9x+1 Find (f/g)(−19)( f / g ) \left( - \frac { 1 } { 9 } \right)(f/g)(−91​)

For the pair of functions, find the indicated domain. -f(x)=2 x-5, g(x)=x+5g ( x ) = \sqrt { x + 5 }g(x)=x+5​ Find the domain of g of. \text { g of. } g of. A) [−∞,0)[ - \infty , 0 )[−∞,0) B) [5,∞)[ 5 , \infty )[5,∞) C) [0,∞)[ 0 , \infty )[0,∞) D) (-5,5)

Determine whether the given function is even, odd, or neither even nor odd. - A) Neither B) Odd C) Even

Graphs, Functions, and Models

Quadratic Functions and Equations; Inequalities

Polynomial and Rational Functions

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Filters

Answer the question. -How can the graph of $f ( x ) = 0.4 ( x + 7 ) ^ { 2 } - 9$ be obtained from the graph of $y = x ^ { 2 } ?$

For the pair of functions, find the indicated domain. - $f ( x ) = 2 x - 5 , g ( x ) = \sqrt { x + 10 }$ Find the domain of f+g

Find f(x) and g(x) such that h(x) = (f g)(x). - $h ( x ) = \left( \frac { x ^ { 3 } + 5 } { 5 - x ^ { 3 } } \right) ^ { 8 }$

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = x ^ { 2 } - 1 , g ( x ) = 9 x + 1$ Find $( f / g ) \left( - \frac { 1 } { 9 } \right)$

For the pair of functions, find the indicated domain. -f(x)=2 x-5, $g ( x ) = \sqrt { x + 5 }$ Find the domain of $\text { g of. }$ A) $[ - \infty , 0 )$ B) $[ 5 , \infty )$ C) $[ 0 , \infty )$ D) (-5,5)