Question 1

Find the composition.
-If $f ( x ) = 2 x + 5$ and $g ( x ) = x + 5$, find $( f \circ g ) ( x )$

Accepted Answer

A)  $2 x ^ { 2 } + 15$ 
B)  $2 x + 10$ 
C)  $2 x ^ { 2 } + 15 x + 25$ 
D)  $2 x + 15$ 
A)  $2 x ^ { 2 } + 15$ 
B)  $2 x + 10$ 
C)  $2 x ^ { 2 } + 15 x + 25$ 
D)  $2 x + 15$

Question 2

Fill in the blank.
-To obtain the graph of f(x)- k, shift the of f(x)k units.

Accepted Answer

A) up 
B) to the left 
C) to the right 
D) down 
A) up 
B) to the left 
C) to the right 
D) down

Question 3

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

Accepted Answer

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

Question 4

Graph the two functions on one coordinate plane.
-$\begin{array}{l}
f(x)=x^{2} \
h(x)=x^{2}-2
\end{array}$

Accepted Answer

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

Question 5

Evaluate the function.
-If $h ( x ) = 2 x - 9$, find $h \left( a ^ { 2 } \right) - h \left( \frac { 1 } { 3 } \right)$

Accepted Answer

A)  $2 a ^ { 2 } - \frac { 29 } { 3 }$ 
B)  $2 a ^ { 2 } - \frac { 2 } { 3 }$ 
C)  $2 a ^ { 2 } - \frac { 2 } { 3 } x - 9$ 
D)  $2 a ^ { 2 } - \frac { 56 } { 3 }$ 
A)  $2 a ^ { 2 } - \frac { 29 } { 3 }$ 
B)  $2 a ^ { 2 } - \frac { 2 } { 3 }$ 
C)  $2 a ^ { 2 } - \frac { 2 } { 3 } x - 9$ 
D)  $2 a ^ { 2 } - \frac { 56 } { 3 }$

Question 6

Perform the requested operation on the given function.
-$$f ( x ) = \sqrt { 2 x } , g ( x ) = - 5 x + 8$$
Find $( f g ) ( x )$.

Accepted Answer

A)  $- 5 x \sqrt { 2 x } + 8 \sqrt { 2 x }$ 
B)  $- 10 x ^ { 2 } + 16$ 
C)  $- 10 x + 8 \sqrt { 2 x }$ 
D)  $\sqrt { 2 \mathrm { x } } + 40 \mathrm { x }$ 
A)  $- 5 x \sqrt { 2 x } + 8 \sqrt { 2 x }$ 
B)  $- 10 x ^ { 2 } + 16$ 
C)  $- 10 x + 8 \sqrt { 2 x }$ 
D)  $\sqrt { 2 \mathrm { x } } + 40 \mathrm { x }$

Question 7

Evaluate the function.
-If $g ( x ) = \frac { 1 } { 3 } x - 2$, find $g ( a + 1 )$

Accepted Answer

A)  $\frac { a + 5 } { 3 }$ 
B)  $\frac { a - 5 } { 3 }$ 
C)  $\frac { a - 11 } { 3 }$ 
D)  $\frac { a - 3 } { 3 }$ 
A)  $\frac { a + 5 } { 3 }$ 
B)  $\frac { a - 5 } { 3 }$ 
C)  $\frac { a - 11 } { 3 }$ 
D)  $\frac { a - 3 } { 3 }$

Question 8

Find the composition.
-If $f ( x ) = 6 x ^ { 2 } - 5 x$ and $g ( x ) = - 3 x$, find $( g \circ f ) ( x )$

Accepted Answer

A)  $- 18 x ^ { 3 } + 15 x ^ { 2 }$ 
B)  $- 18 x ^ { 2 } + 15 x$ 
C)  $6 x ^ { 2 } - 10$ 
D)  $54 x ^ { 2 } - 5 x$ 
A)  $- 18 x ^ { 3 } + 15 x ^ { 2 }$ 
B)  $- 18 x ^ { 2 } + 15 x$ 
C)  $6 x ^ { 2 } - 10$ 
D)  $54 x ^ { 2 } - 5 x$

Question 9

Determine whether or not the graph represents a function.
-

Accepted Answer

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

Question 10

Determine whether or not the graph represents a function.
-

Accepted Answer

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

Question 11

Find the composition.
-If $f ( x ) = \frac { x - 6 } { 4 }$ and $g ( x ) = 4 x + 6$, find $g [ f ( x ) ]$

Accepted Answer

A)  $x$ 
B)  $x - \frac { 3 } { 2 }$ 
C)  $x + 12$ 
D)  $4 x + 18$ 
A)  $x$ 
B)  $x - \frac { 3 } { 2 }$ 
C)  $x + 12$ 
D)  $4 x + 18$

Question 12

Determine whether or not the graph represents a function.
-

Accepted Answer

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

Question 13

Perform the requested operation on the given function.
-$$f ( x ) = - 2 x ^ { 2 } + 6 , g ( x ) = x - 2$$
Find $( f - g ) ( - 4 )$.

Accepted Answer

A)  $- 22$ 
B)  $- 20$ 
C)  $- 28$ 
D)  $- 24$ 
A)  $- 22$ 
B)  $- 20$ 
C)  $- 28$ 
D)  $- 24$

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

Perform the requested operation on the given function.
-$$f ( x ) = 5 x + 2 , g ( x ) = 3 x ^ { 2 } + 4 x + 4$$
Find $\left( \frac { f } { g } \right) ( 5 )$.

Accepted Answer

A) ـــــ 
B)  $-$ 
C) ــــــ 
D)  $- \frac { 3 } { 11 }$ 
A) ـــــ 
B)  $-$ 
C) ــــــ 
D)  $- \frac { 3 } { 11 }$

Question 16

Perform the requested operation on the given function.
-$$f ( x ) = \sqrt { 2 x + 3 } , g ( x ) = \sqrt { 4 x - 25 }$$
Find $( f g ) ( x )$.

Accepted Answer

A)  $( 2 x - 5 ) ( \sqrt { 2 x + 3 } )$ 
B)  $( 2 x + 3 ) ( 4 x - 25 )$ 
C)  $( 2 x + 3 ) ( 2 x - 5 )$ 
D)  $( \sqrt { 2 x + 3 } ) ( \sqrt { 4 x - 25 } )$ 
A)  $( 2 x - 5 ) ( \sqrt { 2 x + 3 } )$ 
B)  $( 2 x + 3 ) ( 4 x - 25 )$ 
C)  $( 2 x + 3 ) ( 2 x - 5 )$ 
D)  $( \sqrt { 2 x + 3 } ) ( \sqrt { 4 x - 25 } )$

Question 17

Graph the two functions on one coordinate plane.
-$\begin{array}{l}
(x)=x^{2} \
(x)=(x-2)^{2}
\end{array}$

Accepted Answer

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

Question 18

Determine whether or not the graph represents a function.
-

Accepted Answer

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

Question 19

Graph the two functions on one coordinate plane.
-$\begin{array}{l}
f(x)=x^{2} \
g(x)=(x+3)^{2}-5
\end{array}$

Accepted Answer

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

Question 20

Graph the two functions on one coordinate plane.
-$\begin{array}{l}
(x)=x^{3} \
5(x)=x^{3}+3
\end{array}$

Accepted Answer

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

Find the composition. -If $f ( x ) = 2 x + 5$ and $g ( x ) = x + 5$ , find $( f \circ g ) ( x )$

Fill in the blank. -To obtain the graph of f(x)- k, shift the of f(x)k units.

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

Graph the two functions on one coordinate plane. - f(x)= h(x)=-2 $Graph the two functions on one coordinate plane. - \begin{array}{l} f(x)=x^{2} \\ h(x)=x^{2}-2 \end{array}$

Evaluate the function. -If $h ( x ) = 2 x - 9$ , find $h \left( a ^ { 2 } \right) - h \left( \frac { 1 } { 3 } \right)$

Perform the requested operation on the given function. - $f ( x ) = \sqrt { 2 x } , g ( x ) = - 5 x + 8$ Find $( f g ) ( x )$ .

Evaluate the function. -If $g ( x ) = \frac { 1 } { 3 } x - 2$ , find $g ( a + 1 )$

Find the composition. -If $f ( x ) = 6 x ^ { 2 } - 5 x$ and $g ( x ) = - 3 x$ , find $( g \circ f ) ( x )$

Determine whether or not the graph represents a function. -

Determine whether or not the graph represents a function. -

Find the composition. -If $f ( x ) = \frac { x - 6 } { 4 }$ and $g ( x ) = 4 x + 6$ , find $g [ f ( x ) ]$

Determine whether or not the graph represents a function. -

Perform the requested operation on the given function. - $f ( x ) = - 2 x ^ { 2 } + 6 , g ( x ) = x - 2$ Find $( f - g ) ( - 4 )$ .

Determine whether or not the graph represents a function. -

Perform the requested operation on the given function. - $f ( x ) = 5 x + 2 , g ( x ) = 3 x ^ { 2 } + 4 x + 4$ Find $\left( \frac { f } { g } \right) ( 5 )$ .

Perform the requested operation on the given function. - $f ( x ) = \sqrt { 2 x + 3 } , g ( x ) = \sqrt { 4 x - 25 }$ Find $( f g ) ( x )$ .

Graph the two functions on one coordinate plane. - (x)= (x)=(x-2 $Graph the two functions on one coordinate plane. - \begin{array}{l} (x)=x^{2} \\ (x)=(x-2)^{2} \end{array}$

Determine whether or not the graph represents a function. -

Graph the two functions on one coordinate plane. - f(x)= g(x)=(x+3-5 $Graph the two functions on one coordinate plane. - \begin{array}{l} f(x)=x^{2} \\ g(x)=(x+3)^{2}-5 \end{array}$

Graph the two functions on one coordinate plane. - (x)= 5(x)=+3 $Graph the two functions on one coordinate plane. - \begin{array}{l} (x)=x^{3} \\ 5(x)=x^{3}+3 \end{array}$

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

Find the composition. -If f(x)=2x+5f ( x ) = 2 x + 5f(x)=2x+5 and g(x)=x+5g ( x ) = x + 5g(x)=x+5 , find (f∘g)(x)( f \circ g ) ( x )(f∘g)(x)

Fill in the blank. -To obtain the graph of f(x)- k, shift the of f(x)k units.

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

Graph the two functions on one coordinate plane. - f(x)= h(x)=-2

Evaluate the function. -If h(x)=2x−9h ( x ) = 2 x - 9h(x)=2x−9 , find h(a2)−h(13)h \left( a ^ { 2 } \right) - h \left( \frac { 1 } { 3 } \right)h(a2)−h(31​)

Perform the requested operation on the given function. - f(x)=2x,g(x)=−5x+8f ( x ) = \sqrt { 2 x } , g ( x ) = - 5 x + 8f(x)=2x​,g(x)=−5x+8 Find (fg)(x)( f g ) ( x )(fg)(x) .

Evaluate the function. -If g(x)=13x−2g ( x ) = \frac { 1 } { 3 } x - 2g(x)=31​x−2 , find g(a+1)g ( a + 1 )g(a+1)

Find the composition. -If f(x)=6x2−5xf ( x ) = 6 x ^ { 2 } - 5 xf(x)=6x2−5x and g(x)=−3xg ( x ) = - 3 xg(x)=−3x , find (g∘f)(x)( g \circ f ) ( x )(g∘f)(x)

Determine whether or not the graph represents a function. -

Determine whether or not the graph represents a function. -

Find the composition. -If f(x)=x−64f ( x ) = \frac { x - 6 } { 4 }f(x)=4x−6​ and g(x)=4x+6g ( x ) = 4 x + 6g(x)=4x+6 , find g[f(x)]g [ f ( x ) ]g[f(x)]

Determine whether or not the graph represents a function. -

Perform the requested operation on the given function. - f(x)=−2x2+6,g(x)=x−2f ( x ) = - 2 x ^ { 2 } + 6 , g ( x ) = x - 2f(x)=−2x2+6,g(x)=x−2 Find (f−g)(−4)( f - g ) ( - 4 )(f−g)(−4) .

Determine whether or not the graph represents a function. -

Perform the requested operation on the given function. - f(x)=5x+2,g(x)=3x2+4x+4f ( x ) = 5 x + 2 , g ( x ) = 3 x ^ { 2 } + 4 x + 4f(x)=5x+2,g(x)=3x2+4x+4 Find (fg)(5)\left( \frac { f } { g } \right) ( 5 )(gf​)(5) .

Perform the requested operation on the given function. - f(x)=2x+3,g(x)=4x−25f ( x ) = \sqrt { 2 x + 3 } , g ( x ) = \sqrt { 4 x - 25 }f(x)=2x+3​,g(x)=4x−25​ Find (fg)(x)( f g ) ( x )(fg)(x) .

Graph the two functions on one coordinate plane. - (x)= (x)=(x-2

Determine whether or not the graph represents a function. -

Graph the two functions on one coordinate plane. - f(x)= g(x)=(x+3-5

Graph the two functions on one coordinate plane. - (x)= 5(x)=+3

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

Find the composition. -If $f ( x ) = 2 x + 5$ and $g ( x ) = x + 5$ , find $( f \circ g ) ( x )$

Graph the two functions on one coordinate plane. - f(x)= h(x)=-2 $Graph the two functions on one coordinate plane. - \begin{array}{l} f(x)=x^{2} \\ h(x)=x^{2}-2 \end{array}$

Evaluate the function. -If $h ( x ) = 2 x - 9$ , find $h \left( a ^ { 2 } \right) - h \left( \frac { 1 } { 3 } \right)$

Perform the requested operation on the given function. - $f ( x ) = \sqrt { 2 x } , g ( x ) = - 5 x + 8$ Find $( f g ) ( x )$ .

Evaluate the function. -If $g ( x ) = \frac { 1 } { 3 } x - 2$ , find $g ( a + 1 )$

Find the composition. -If $f ( x ) = 6 x ^ { 2 } - 5 x$ and $g ( x ) = - 3 x$ , find $( g \circ f ) ( x )$

Find the composition. -If $f ( x ) = \frac { x - 6 } { 4 }$ and $g ( x ) = 4 x + 6$ , find $g [ f ( x ) ]$

Perform the requested operation on the given function. - $f ( x ) = - 2 x ^ { 2 } + 6 , g ( x ) = x - 2$ Find $( f - g ) ( - 4 )$ .

Perform the requested operation on the given function. - $f ( x ) = 5 x + 2 , g ( x ) = 3 x ^ { 2 } + 4 x + 4$ Find $\left( \frac { f } { g } \right) ( 5 )$ .

Perform the requested operation on the given function. - $f ( x ) = \sqrt { 2 x + 3 } , g ( x ) = \sqrt { 4 x - 25 }$ Find $( f g ) ( x )$ .

Graph the two functions on one coordinate plane. - (x)= (x)=(x-2 $Graph the two functions on one coordinate plane. - \begin{array}{l} (x)=x^{2} \\ (x)=(x-2)^{2} \end{array}$

Graph the two functions on one coordinate plane. - f(x)= g(x)=(x+3-5 $Graph the two functions on one coordinate plane. - \begin{array}{l} f(x)=x^{2} \\ g(x)=(x+3)^{2}-5 \end{array}$

Graph the two functions on one coordinate plane. - (x)= 5(x)=+3 $Graph the two functions on one coordinate plane. - \begin{array}{l} (x)=x^{3} \\ 5(x)=x^{3}+3 \end{array}$