Question 1

Evaluate the function.
-If $f ( x ) = - 9 x + 4$, find $f ( - 3 )$

Accepted Answer

A)  31 
B)  $- 5$ 
C)  23 
D)  15 
A)  31 
B)  $- 5$ 
C)  23 
D)  15 A

Question 2

Determine whether or not the graph represents a function.
-

Accepted Answer

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

Question 3

Perform the requested operation on the given function.
-$$f ( x ) = 2 - 9 x , g ( x ) = - 6 x + 9$$
Find $( f + g ) ( x )$.

Accepted Answer

A)  $- 6 x + 2$ 
B)  $- 15 x + 11$ 
C)  $- 3 x + 11$ 
D)  $- 4 x$ 
A)  $- 6 x + 2$ 
B)  $- 15 x + 11$ 
C)  $- 3 x + 11$ 
D)  $- 4 x$ B

Question 4

Solve
-A wind turbine generator produces P kilowatts of power for wind speed w (measured in miles per hour) according to the equation $\mathrm { P } = 2.6 \mathrm { w } ^ { 2 }$. Thus, the number of kilowatt hours $\mathrm { P }$ as a function of $\mathrm { w }$ is $\mathrm { P } ( \mathrm { w } ) = 2.6 \mathrm { w } ^ { 2 }$. At a particular time the wind speed is measured to be 20 miles per hour. However, the measuring device is known to have an inherent error of measure, e. Find an expression for the actual amount of energy produced by finding $\mathrm { P } ( 20 + \mathrm { e } )$.

Accepted Answer

A)  $\mathrm { P } ( 20 + \mathrm { e } ) = 2.6 \mathrm { e } ^ { 2 } + 20$ 
B)  $\mathrm { P } ( 20 + \mathrm { e } ) = 2.6 \mathrm { e } ^ { 2 } + 1040$ 
C)  $\mathrm { P } ( 20 + \mathrm { e } ) = 2 \cdot 6 \mathrm { e } ^ { 2 } + 104 \mathrm { e } + 1040$ 
D)  $\mathrm { P } ( 20 + \mathrm { e } ) = \mathrm { e } + 1040$ 
A)  $\mathrm { P } ( 20 + \mathrm { e } ) = 2.6 \mathrm { e } ^ { 2 } + 20$ 
B)  $\mathrm { P } ( 20 + \mathrm { e } ) = 2.6 \mathrm { e } ^ { 2 } + 1040$ 
C)  $\mathrm { P } ( 20 + \mathrm { e } ) = 2 \cdot 6 \mathrm { e } ^ { 2 } + 104 \mathrm { e } + 1040$ 
D)  $\mathrm { P } ( 20 + \mathrm { e } ) = \mathrm { e } + 1040$

Question 5

Find the composition.
-If $f ( x ) = x ^ { 2 } + 4 x$ and $g ( x ) = x + 2$, find $( g \circ f ) ( 4 )$

Accepted Answer

A)  192 
B)  60 
C)  34 
D)  36 
A)  192 
B)  60 
C)  34 
D)  36

Question 6

Indicate whether the graph represents a one-to-one function
-

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 7

Perform the requested operation on the given function.
-$$f ( x ) = 2 x - 8 , g ( x ) = 8 x - 3$$
Find $( f - g ) ( x )$.

Accepted Answer

A)  $10 x - 11$ 
B)  $- 6 x - 11$ 
C)  $x + 5$ 
D)  $- 6 x - 5$ 
A)  $10 x - 11$ 
B)  $- 6 x - 11$ 
C)  $x + 5$ 
D)  $- 6 x - 5$

Question 8

Indicate whether the graph represents a one-to-one function
-

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 9

Perform the requested operation on the given function.
-$$f ( x ) = 2 x ^ { 2 } - 7 x , g ( x ) = x ^ { 2 } - 4 x - 21$$
Find $\left( \frac { f } { g } \right) ( x )$.

Accepted Answer

A)  $\frac { 2 x - 7 } { - 4 }$ 
B)  $\frac { 2 x } { x + 1 }$ 
C)  $\frac { 2 - x } { 21 }$ 
D)  $\frac { 2 x ^ { 2 } - 7 x } { x ^ { 2 } - 4 x - 21 }$ 
A)  $\frac { 2 x - 7 } { - 4 }$ 
B)  $\frac { 2 x } { x + 1 }$ 
C)  $\frac { 2 - x } { 21 }$ 
D)  $\frac { 2 x ^ { 2 } - 7 x } { x ^ { 2 } - 4 x - 21 }$

Question 10

Perform the requested operation on the given function.
-$$f ( x ) = 2 x - 8 , g ( x ) = 6 x - 5$$
Find $( g - f ) ( x )$.

Accepted Answer

A)  $x - 13$ 
B)  $- 4 x - 13$ 
C)  $x + 3$ 
D)  $- 4 x - 3$ 
A)  $x - 13$ 
B)  $- 4 x - 13$ 
C)  $x + 3$ 
D)  $- 4 x - 3$

Question 11

Determine whether or not the graph represents a function.
-

Accepted Answer

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

Question 12

Find the composition.
-If $f ( x ) = x ^ { 2 } + 2 x$ and $g ( x ) = x + 4$, find $( f \circ g ) ( 4 )$

Accepted Answer

A)  0 
B)  $2 \sqrt { 3 }$ 
C)  28 
D)  80 
A)  0 
B)  $2 \sqrt { 3 }$ 
C)  28 
D)  80

Question 13

Indicate whether the function is one-to-one.

-$$C = \{ ( 7 - 5 ) , ( 5 - 7 ) , ( 2,3 ) , ( - 2 , - 3 ) \}$$

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 14

Determine whether or not the graph represents a function.
-

Accepted Answer

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

Question 15

Graph the two functions on one coordinate plane.
-$\begin{array}{l}
f(x)=|x| \
5(x)=|x|-5
\end{array}$

Accepted Answer

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

Question 16

Find the composition.
-If $f ( x ) = 4 x ^ { 2 } + 2 x + 4$ and $g ( x ) = 2 x - 7$, find $g [ f ( x ) ]$

Accepted Answer

A)  $4 x ^ { 2 } + 4 x + 1$ 
B)  $8 x ^ { 2 } + 4 x + 15$ 
C)  $8 x ^ { 2 } + 4 x + 1$ 
D)  $4 x ^ { 2 } + 2 x - 3$ 
A)  $4 x ^ { 2 } + 4 x + 1$ 
B)  $8 x ^ { 2 } + 4 x + 15$ 
C)  $8 x ^ { 2 } + 4 x + 1$ 
D)  $4 x ^ { 2 } + 2 x - 3$

Question 17

Evaluate the function.
-If $g ( x ) = 4 x - 2$, find $g ( a - 1 )$

Accepted Answer

A)  $4 a - 8$ 
B)  $4 a - 6$ 
C)  $4 a - 4$ 
D)  $4 a - 3$ 
A)  $4 a - 8$ 
B)  $4 a - 6$ 
C)  $4 a - 4$ 
D)  $4 a - 3$

Question 18

Indicate whether the graph represents a one-to-one function
-

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 19

Evaluate the function.
-If $g ( x ) = 5 x - 3$, find $g ( a ) + g ( - 1 )$

Accepted Answer

A)  $5 \mathrm { a } - 11$ 
B)  $5 a - 5$ 
C)  $5 a - 4$ 
D)  $5 a - 8$ 
A)  $5 \mathrm { a } - 11$ 
B)  $5 a - 5$ 
C)  $5 a - 4$ 
D)  $5 a - 8$

Question 20

Find the composition.
-If $f ( x ) = - 3 x - 4$ and $g ( x ) = \frac { 1 } { x }$, find $g \left[ f \left( \frac { 1 } { 4 } \right] \right.$.

Accepted Answer

A)  $- \frac { 19 } { 4 }$ 
B)  $- 16$ 
C)  $- \frac { 4 } { 19 }$ 
D)  $- \frac { 1 } { 19 }$ 
A)  $- \frac { 19 } { 4 }$ 
B)  $- 16$ 
C)  $- \frac { 4 } { 19 }$ 
D)  $- \frac { 1 } { 19 }$

Evaluate the function. -If $f ( x ) = - 9 x + 4$ , find $f ( - 3 )$

Determine whether or not the graph represents a function. -

Perform the requested operation on the given function. - $f ( x ) = 2 - 9 x , g ( x ) = - 6 x + 9$ Find $( f + g ) ( x )$ .

Find the composition. -If $f ( x ) = x ^ { 2 } + 4 x$ and $g ( x ) = x + 2$ , find $( g \circ f ) ( 4 )$

Indicate whether the graph represents a one-to-one function -

Perform the requested operation on the given function. - $f ( x ) = 2 x - 8 , g ( x ) = 8 x - 3$ Find $( f - g ) ( x )$ .

Indicate whether the graph represents a one-to-one function -

Perform the requested operation on the given function. - $f ( x ) = 2 x ^ { 2 } - 7 x , g ( x ) = x ^ { 2 } - 4 x - 21$ Find $\left( \frac { f } { g } \right) ( x )$ .

Perform the requested operation on the given function. - $f ( x ) = 2 x - 8 , g ( x ) = 6 x - 5$ Find $( g - f ) ( x )$ .

Determine whether or not the graph represents a function. -

Find the composition. -If $f ( x ) = x ^ { 2 } + 2 x$ and $g ( x ) = x + 4$ , find $( f \circ g ) ( 4 )$

Indicate whether the function is one-to-one. - $C = \{ ( 7 - 5 ) , ( 5 - 7 ) , ( 2,3 ) , ( - 2 , - 3 ) \}$

Determine whether or not the graph represents a function. -

Graph the two functions on one coordinate plane. - f(x)=|x| 5(x)=|x|-5 $Graph the two functions on one coordinate plane. - \begin{array}{l} f(x)=|x| \\ 5(x)=|x|-5 \end{array}$

Find the composition. -If $f ( x ) = 4 x ^ { 2 } + 2 x + 4$ and $g ( x ) = 2 x - 7$ , find $g [ f ( x ) ]$

Evaluate the function. -If $g ( x ) = 4 x - 2$ , find $g ( a - 1 )$

Indicate whether the graph represents a one-to-one function -

Evaluate the function. -If $g ( x ) = 5 x - 3$ , find $g ( a ) + g ( - 1 )$

Find the composition. -If $f ( x ) = - 3 x - 4$ and $g ( x ) = \frac { 1 } { x }$ , find $g \left[ f \left( \frac { 1 } { 4 } \right] \right.$ .

Real Numbers and Variables

Equations, Inequalities, and Applications

Graphing and Functions

Systems of Linear Equations and Inequalities

Exponents and Polynomials

Factoring

Rational Expressions and Equations

Rational Exponents and Radicals

Quadratic Equations and Inequalities

The Conic Sections

Logarithmic and Exponential Functions

Filters

Exam 11: Additional Properties of Functions

Evaluate the function. -If f(x)=−9x+4f ( x ) = - 9 x + 4f(x)=−9x+4 , find f(−3)f ( - 3 )f(−3)

Determine whether or not the graph represents a function. -

Perform the requested operation on the given function. - f(x)=2−9x,g(x)=−6x+9f ( x ) = 2 - 9 x , g ( x ) = - 6 x + 9f(x)=2−9x,g(x)=−6x+9 Find (f+g)(x)( f + g ) ( x )(f+g)(x) .

Find the composition. -If f(x)=x2+4xf ( x ) = x ^ { 2 } + 4 xf(x)=x2+4x and g(x)=x+2g ( x ) = x + 2g(x)=x+2 , find (g∘f)(4)( g \circ f ) ( 4 )(g∘f)(4)

Indicate whether the graph represents a one-to-one function -

Perform the requested operation on the given function. - f(x)=2x−8,g(x)=8x−3f ( x ) = 2 x - 8 , g ( x ) = 8 x - 3f(x)=2x−8,g(x)=8x−3 Find (f−g)(x)( f - g ) ( x )(f−g)(x) .

Indicate whether the graph represents a one-to-one function -

Perform the requested operation on the given function. - f(x)=2x2−7x,g(x)=x2−4x−21f ( x ) = 2 x ^ { 2 } - 7 x , g ( x ) = x ^ { 2 } - 4 x - 21f(x)=2x2−7x,g(x)=x2−4x−21 Find (fg)(x)\left( \frac { f } { g } \right) ( x )(gf​)(x) .

Perform the requested operation on the given function. - f(x)=2x−8,g(x)=6x−5f ( x ) = 2 x - 8 , g ( x ) = 6 x - 5f(x)=2x−8,g(x)=6x−5 Find (g−f)(x)( g - f ) ( x )(g−f)(x) .

Determine whether or not the graph represents a function. -

Find the composition. -If f(x)=x2+2xf ( x ) = x ^ { 2 } + 2 xf(x)=x2+2x and g(x)=x+4g ( x ) = x + 4g(x)=x+4 , find (f∘g)(4)( f \circ g ) ( 4 )(f∘g)(4)

Indicate whether the function is one-to-one. - C={(7−5),(5−7),(2,3),(−2,−3)}C = \{ ( 7 - 5 ) , ( 5 - 7 ) , ( 2,3 ) , ( - 2 , - 3 ) \}C={(7−5),(5−7),(2,3),(−2,−3)}

Determine whether or not the graph represents a function. -

Graph the two functions on one coordinate plane. - f(x)=|x| 5(x)=|x|-5

Find the composition. -If f(x)=4x2+2x+4f ( x ) = 4 x ^ { 2 } + 2 x + 4f(x)=4x2+2x+4 and g(x)=2x−7g ( x ) = 2 x - 7g(x)=2x−7 , find g[f(x)]g [ f ( x ) ]g[f(x)]

Evaluate the function. -If g(x)=4x−2g ( x ) = 4 x - 2g(x)=4x−2 , find g(a−1)g ( a - 1 )g(a−1)

Indicate whether the graph represents a one-to-one function -

Evaluate the function. -If g(x)=5x−3g ( x ) = 5 x - 3g(x)=5x−3 , find g(a)+g(−1)g ( a ) + g ( - 1 )g(a)+g(−1)

Find the composition. -If f(x)=−3x−4f ( x ) = - 3 x - 4f(x)=−3x−4 and g(x)=1xg ( x ) = \frac { 1 } { x }g(x)=x1​ , find g[f(14]g \left[ f \left( \frac { 1 } { 4 } \right] \right.g[f(41​] .

Real Numbers and Variables

Equations, Inequalities, and Applications

Graphing and Functions

Systems of Linear Equations and Inequalities

Exponents and Polynomials

Factoring

Rational Expressions and Equations

Rational Exponents and Radicals

Quadratic Equations and Inequalities

The Conic Sections

Logarithmic and Exponential Functions

Filters

Evaluate the function. -If $f ( x ) = - 9 x + 4$ , find $f ( - 3 )$

Perform the requested operation on the given function. - $f ( x ) = 2 - 9 x , g ( x ) = - 6 x + 9$ Find $( f + g ) ( x )$ .

Find the composition. -If $f ( x ) = x ^ { 2 } + 4 x$ and $g ( x ) = x + 2$ , find $( g \circ f ) ( 4 )$

Perform the requested operation on the given function. - $f ( x ) = 2 x - 8 , g ( x ) = 8 x - 3$ Find $( f - g ) ( x )$ .

Perform the requested operation on the given function. - $f ( x ) = 2 x ^ { 2 } - 7 x , g ( x ) = x ^ { 2 } - 4 x - 21$ Find $\left( \frac { f } { g } \right) ( x )$ .

Perform the requested operation on the given function. - $f ( x ) = 2 x - 8 , g ( x ) = 6 x - 5$ Find $( g - f ) ( x )$ .

Find the composition. -If $f ( x ) = x ^ { 2 } + 2 x$ and $g ( x ) = x + 4$ , find $( f \circ g ) ( 4 )$

Indicate whether the function is one-to-one. - $C = \{ ( 7 - 5 ) , ( 5 - 7 ) , ( 2,3 ) , ( - 2 , - 3 ) \}$

Graph the two functions on one coordinate plane. - f(x)=|x| 5(x)=|x|-5 $Graph the two functions on one coordinate plane. - \begin{array}{l} f(x)=|x| \\ 5(x)=|x|-5 \end{array}$

Find the composition. -If $f ( x ) = 4 x ^ { 2 } + 2 x + 4$ and $g ( x ) = 2 x - 7$ , find $g [ f ( x ) ]$

Evaluate the function. -If $g ( x ) = 4 x - 2$ , find $g ( a - 1 )$

Evaluate the function. -If $g ( x ) = 5 x - 3$ , find $g ( a ) + g ( - 1 )$

Find the composition. -If $f ( x ) = - 3 x - 4$ and $g ( x ) = \frac { 1 } { x }$ , find $g \left[ f \left( \frac { 1 } { 4 } \right] \right.$ .