Question 1

Indicate whether the function is one-to-one.

-$$A = \{ ( 2,17 ) , ( 17,13 ) , ( 3 , - 18 ) \}$$

Accepted Answer

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

Question 2

Indicate whether the function is one-to-one.

-$$B = \{ ( 4,2 ) , ( 5,2 ) , ( 6,8 ) , ( 7,4 ) \}$$

Accepted Answer

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

Question 3

Graph the two functions on one coordinate plane.
-$\begin{array}{l}
(x)=x^{3} \
(x)=(x+5)^{3}+7
\end{array}$

Accepted Answer

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

Question 4

Perform the requested operation on the given function.
-$$f ( x ) = 6 x - 7 , g ( x ) = 3 x - 5$$
Find $( \mathrm { fg } ) ( \mathrm { x } )$.

Accepted Answer

A)  $18 x ^ { 2 } + 35$ 
B)  $18 x ^ { 2 } - 26 x + 35$ 
C)  $9 x ^ { 2 } - 51 x - 12$ 
D)  $18 x ^ { 2 } - 51 x + 35$ 
A)  $18 x ^ { 2 } + 35$ 
B)  $18 x ^ { 2 } - 26 x + 35$ 
C)  $9 x ^ { 2 } - 51 x - 12$ 
D)  $18 x ^ { 2 } - 51 x + 35$

Question 5

Find the composition.
-If $f ( x ) = \sqrt { x + 9 }$ and $g ( x ) = 8 x - 13$, find $f [ g ( x ) ]$

Accepted Answer

A)  $2 \sqrt { 2 x - 1 }$ 
B)  $8 \sqrt { x - 4 }$ 
C)  $2 \sqrt { 2 x + 1 }$ 
D)  $8 \sqrt { x + 9 } - 13$ 
A)  $2 \sqrt { 2 x - 1 }$ 
B)  $8 \sqrt { x - 4 }$ 
C)  $2 \sqrt { 2 x + 1 }$ 
D)  $8 \sqrt { x + 9 } - 13$

Question 6

Evaluate the function.
-If $f ( x ) = 5 x ^ { 2 } + 3 x - 4$, find $f ( k - 1 )$

Accepted Answer

A)  $- 7 k ^ { 2 } + 5 k - 2$ 
B)  $5 k ^ { 2 } - 17 k + 4$ 
C)  $5 \mathrm { k } ^ { 2 } - 7 \mathrm { k } + 4$ 
D)  $5 \mathrm { k } ^ { 2 } - 7 \mathrm { k } - 2$ 
A)  $- 7 k ^ { 2 } + 5 k - 2$ 
B)  $5 k ^ { 2 } - 17 k + 4$ 
C)  $5 \mathrm { k } ^ { 2 } - 7 \mathrm { k } + 4$ 
D)  $5 \mathrm { k } ^ { 2 } - 7 \mathrm { k } - 2$

Question 7

Graph the two functions on one coordinate plane.
-$$f ( x ) = \frac { 3 } { x }$$
$$g ( x ) = \frac { 3 } { x } + 4$$

Accepted Answer

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

Question 8

Find the composition.
-If $f ( x ) = x ^ { 2 } - 1$ and $h ( x ) = \sqrt { x + 7 }$, find $( h \circ f ) ( - 3 )$

Accepted Answer

A) $\sqrt { 9 }$ 
B)  $\sqrt { 15 }$ 
C)  $- 3 \sqrt { 6 }$ 
D)  $2 + \sqrt { 7 }$ 
A) $\sqrt { 9 }$ 
B)  $\sqrt { 15 }$ 
C)  $- 3 \sqrt { 6 }$ 
D)  $2 + \sqrt { 7 }$

Question 9

Perform the requested operation on the given function.
-$$f ( x ) = x + 3 , g ( x ) = x - 4$$
Find $( f + g ) ( - 5 )$.

Accepted Answer

A)  $- 3$ 
B)  $- 11$ 
C)  $- 17$ 
D)  $- 9$ 
A)  $- 3$ 
B)  $- 11$ 
C)  $- 17$ 
D)  $- 9$

Question 10

Perform the requested operation on the given function.
-$$f ( x ) = x + 3 , g ( x ) = 5 x ^ { 2 } + 13 x + 6$$
Find $( f g ) ( - 4 )$.

Accepted Answer

A)  $- 38$ 
B)  $- 34$ 
C)  $- 238$ 
D)  $- 602$ 
A)  $- 38$ 
B)  $- 34$ 
C)  $- 238$ 
D)  $- 602$

Question 11

Indicate whether the function is one-to-one.
-The population $\mathrm { P }$ of a predator mammal depends upon the number $\mathrm { x }$ of a smaller animal that is its primary food source. The population s of the smaller animal depends upon the amount a of a certain plant that is its primary food source. If $\mathrm { P } ( \mathrm { x } ) = 3 \mathrm { x } ^ { 2 } + 8$ and $s ( a ) = 4 a + 4$, what is the relationship between the predator mammal and the plant food source?

Accepted Answer

A)  $\mathrm { P } ( \mathrm { s } ( \mathrm { a } ) ) = 48 \mathrm { a } ^ { 2 } + 96 \mathrm { a } + 56$ 
B)  $\mathrm { P } ( \mathrm { s } ( \mathrm { a } ) ) = 48 \mathrm { a } ^ { 2 } + 48 \mathrm { a } + 56$ 
C)  $\mathrm { P } ( \mathrm { s } ( \mathrm { a } ) ) = 16 \mathrm { a } ^ { 2 } + 32 \mathrm { a } + 24$ 
D)  $\mathrm { P } ( \mathrm { s } ( \mathrm { a } ) ) = 12 \mathrm { a } + 12$ 
A)  $\mathrm { P } ( \mathrm { s } ( \mathrm { a } ) ) = 48 \mathrm { a } ^ { 2 } + 96 \mathrm { a } + 56$ 
B)  $\mathrm { P } ( \mathrm { s } ( \mathrm { a } ) ) = 48 \mathrm { a } ^ { 2 } + 48 \mathrm { a } + 56$ 
C)  $\mathrm { P } ( \mathrm { s } ( \mathrm { a } ) ) = 16 \mathrm { a } ^ { 2 } + 32 \mathrm { a } + 24$ 
D)  $\mathrm { P } ( \mathrm { s } ( \mathrm { a } ) ) = 12 \mathrm { a } + 12$

Question 12

Evaluate the function.
-If $p ( x ) = 4 x ^ { 2 } + 3 x - 1$, find $p \left( - \frac { a ^ { 2 } } { 4 } \right)$

Accepted Answer

A)  $- a ^ { 4 } - 3 a ^ { 2 } - \frac { 1 } { 4 }$ 
B)  $a ^ { 4 } - \frac { 3 a ^ { 2 } } { 4 } - 1$ 
C)  $\frac { a ^ { 4 } } { 4 } - \frac { 3 a ^ { 2 } } { 4 } - 1$ 
D)  $\frac { - a ^ { 4 } - 3 a ^ { 2 } - 1 } { 4 }$ 
A)  $- a ^ { 4 } - 3 a ^ { 2 } - \frac { 1 } { 4 }$ 
B)  $a ^ { 4 } - \frac { 3 a ^ { 2 } } { 4 } - 1$ 
C)  $\frac { a ^ { 4 } } { 4 } - \frac { 3 a ^ { 2 } } { 4 } - 1$ 
D)  $\frac { - a ^ { 4 } - 3 a ^ { 2 } - 1 } { 4 }$

Question 13

Find the composition.
-If $f ( x ) = x ^ { 2 } - 6$ and $h ( x ) = \sqrt { x + 13 }$, find $( h \circ f ) ( - 4 )$

Accepted Answer

A)  $- 2 + \sqrt { 13 }$ 
B)  3 
C)  $- 4 \sqrt { 7 }$ 
D)  $\sqrt { 23 }$ 
A)  $- 2 + \sqrt { 13 }$ 
B)  3 
C)  $- 4 \sqrt { 7 }$ 
D)  $\sqrt { 23 }$

Question 14

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

Accepted Answer

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

Question 15

Evaluate the function.
-If $f ( x ) = x ^ { 2 } - 2$, find $f ( a - 3 )$.

Accepted Answer

A)  $a ^ { 2 } - 6 a + 9$ 
B)  $a ^ { 2 } - 5$ 
C)  $a ^ { 2 } - 6 a + 7$ 
D)  $a ^ { 2 } + 9$ 
A)  $a ^ { 2 } - 6 a + 9$ 
B)  $a ^ { 2 } - 5$ 
C)  $a ^ { 2 } - 6 a + 7$ 
D)  $a ^ { 2 } + 9$

Question 16

Find the composition.
-If $f ( x ) = 6 x + 2$ and $g ( x ) = x + 4$, find $( g \circ f ) ( x )$

Accepted Answer

A)  $6 x + 6$ 
B)  $6 x ^ { 2 } + 26 x + 8$ 
C)  $6 x + 26$ 
D)  $6 x ^ { 2 } + 26$ 
A)  $6 x + 6$ 
B)  $6 x ^ { 2 } + 26 x + 8$ 
C)  $6 x + 26$ 
D)  $6 x ^ { 2 } + 26$

Question 17

Determine whether or not the graph represents a function.
-

Accepted Answer

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

Question 18

Graph the two functions on one coordinate plane.
-$\begin{array}{l}
(x)=|x| \
y(x)=|x-4|+1
\end{array}$

Accepted Answer

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

Question 19

Perform the requested operation on the given function.
-$$f ( x ) = 2 x ^ { 2 } - 7 x - 6 , g ( x ) = - 7 x + 2$$
Find $( f + g ) ( - 4 )$.

Accepted Answer

A)  $- 56$ 
B)  84 
C)  $- 66$ 
A)  $- 56$ 
B)  84 
C)  $- 66$

Question 20

Determine whether or not the graph represents a function.
-

Accepted Answer

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

Indicate whether the function is one-to-one. - $A = \{ ( 2,17 ) , ( 17,13 ) , ( 3 , - 18 ) \}$

Indicate whether the function is one-to-one. - $B = \{ ( 4,2 ) , ( 5,2 ) , ( 6,8 ) , ( 7,4 ) \}$

Graph the two functions on one coordinate plane. - (x)= (x)=(x+5+7 $Graph the two functions on one coordinate plane. - \begin{array}{l} (x)=x^{3} \\ (x)=(x+5)^{3}+7 \end{array}$

Perform the requested operation on the given function. - $f ( x ) = 6 x - 7 , g ( x ) = 3 x - 5$ Find $( \mathrm { fg } ) ( \mathrm { x } )$ .

Find the composition. -If $f ( x ) = \sqrt { x + 9 }$ and $g ( x ) = 8 x - 13$ , find $f [ g ( x ) ]$

Evaluate the function. -If $f ( x ) = 5 x ^ { 2 } + 3 x - 4$ , find $f ( k - 1 )$

Graph the two functions on one coordinate plane. - $f ( x ) = \frac { 3 } { x }$ $g ( x ) = \frac { 3 } { x } + 4$ $Graph the two functions on one coordinate plane. - f ( x ) = \frac { 3 } { x } g ( x ) = \frac { 3 } { x } + 4$

Find the composition. -If $f ( x ) = x ^ { 2 } - 1$ and $h ( x ) = \sqrt { x + 7 }$ , find $( h \circ f ) ( - 3 )$

Perform the requested operation on the given function. - $f ( x ) = x + 3 , g ( x ) = x - 4$ Find $( f + g ) ( - 5 )$ .

Perform the requested operation on the given function. - $f ( x ) = x + 3 , g ( x ) = 5 x ^ { 2 } + 13 x + 6$ Find $( f g ) ( - 4 )$ .

Evaluate the function. -If $p ( x ) = 4 x ^ { 2 } + 3 x - 1$ , find $p \left( - \frac { a ^ { 2 } } { 4 } \right)$

Find the composition. -If $f ( x ) = x ^ { 2 } - 6$ and $h ( x ) = \sqrt { x + 13 }$ , find $( h \circ f ) ( - 4 )$

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

Evaluate the function. -If $f ( x ) = x ^ { 2 } - 2$ , find $f ( a - 3 )$ .

Find the composition. -If $f ( x ) = 6 x + 2$ and $g ( x ) = x + 4$ , find $( g \circ f ) ( x )$

Determine whether or not the graph represents a function. -

Graph the two functions on one coordinate plane. - (x)=|x| y(x)=|x-4|+1 $Graph the two functions on one coordinate plane. - \begin{array}{l} (x)=|x| \\ y(x)=|x-4|+1 \end{array}$

Perform the requested operation on the given function. - $f ( x ) = 2 x ^ { 2 } - 7 x - 6 , g ( x ) = - 7 x + 2$ Find $( f + g ) ( - 4 )$ .

Determine whether or not the graph represents a function. -

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

Indicate whether the function is one-to-one. - A={(2,17),(17,13),(3,−18)}A = \{ ( 2,17 ) , ( 17,13 ) , ( 3 , - 18 ) \}A={(2,17),(17,13),(3,−18)}

Indicate whether the function is one-to-one. - B={(4,2),(5,2),(6,8),(7,4)}B = \{ ( 4,2 ) , ( 5,2 ) , ( 6,8 ) , ( 7,4 ) \}B={(4,2),(5,2),(6,8),(7,4)}

Graph the two functions on one coordinate plane. - (x)= (x)=(x+5+7

Perform the requested operation on the given function. - f(x)=6x−7,g(x)=3x−5f ( x ) = 6 x - 7 , g ( x ) = 3 x - 5f(x)=6x−7,g(x)=3x−5 Find (fg)(x)( \mathrm { fg } ) ( \mathrm { x } )(fg)(x) .

Find the composition. -If f(x)=x+9f ( x ) = \sqrt { x + 9 }f(x)=x+9​ and g(x)=8x−13g ( x ) = 8 x - 13g(x)=8x−13 , find f[g(x)]f [ g ( x ) ]f[g(x)]

Evaluate the function. -If f(x)=5x2+3x−4f ( x ) = 5 x ^ { 2 } + 3 x - 4f(x)=5x2+3x−4 , find f(k−1)f ( k - 1 )f(k−1)

Graph the two functions on one coordinate plane. - f(x)=3xf ( x ) = \frac { 3 } { x }f(x)=x3​ g(x)=3x+4g ( x ) = \frac { 3 } { x } + 4g(x)=x3​+4

Find the composition. -If f(x)=x2−1f ( x ) = x ^ { 2 } - 1f(x)=x2−1 and h(x)=x+7h ( x ) = \sqrt { x + 7 }h(x)=x+7​ , find (h∘f)(−3)( h \circ f ) ( - 3 )(h∘f)(−3)

Perform the requested operation on the given function. - f(x)=x+3,g(x)=x−4f ( x ) = x + 3 , g ( x ) = x - 4f(x)=x+3,g(x)=x−4 Find (f+g)(−5)( f + g ) ( - 5 )(f+g)(−5) .

Perform the requested operation on the given function. - f(x)=x+3,g(x)=5x2+13x+6f ( x ) = x + 3 , g ( x ) = 5 x ^ { 2 } + 13 x + 6f(x)=x+3,g(x)=5x2+13x+6 Find (fg)(−4)( f g ) ( - 4 )(fg)(−4) .

Evaluate the function. -If p(x)=4x2+3x−1p ( x ) = 4 x ^ { 2 } + 3 x - 1p(x)=4x2+3x−1 , find p(−a24)p \left( - \frac { a ^ { 2 } } { 4 } \right)p(−4a2​)

Find the composition. -If f(x)=x2−6f ( x ) = x ^ { 2 } - 6f(x)=x2−6 and h(x)=x+13h ( x ) = \sqrt { x + 13 }h(x)=x+13​ , find (h∘f)(−4)( h \circ f ) ( - 4 )(h∘f)(−4)

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

Evaluate the function. -If f(x)=x2−2f ( x ) = x ^ { 2 } - 2f(x)=x2−2 , find f(a−3)f ( a - 3 )f(a−3) .

Find the composition. -If f(x)=6x+2f ( x ) = 6 x + 2f(x)=6x+2 and g(x)=x+4g ( x ) = x + 4g(x)=x+4 , find (g∘f)(x)( g \circ f ) ( x )(g∘f)(x)

Determine whether or not the graph represents a function. -

Graph the two functions on one coordinate plane. - (x)=|x| y(x)=|x-4|+1

Perform the requested operation on the given function. - f(x)=2x2−7x−6,g(x)=−7x+2f ( x ) = 2 x ^ { 2 } - 7 x - 6 , g ( x ) = - 7 x + 2f(x)=2x2−7x−6,g(x)=−7x+2 Find (f+g)(−4)( f + g ) ( - 4 )(f+g)(−4) .

Determine whether or not the graph represents a function. -

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

Indicate whether the function is one-to-one. - $A = \{ ( 2,17 ) , ( 17,13 ) , ( 3 , - 18 ) \}$

Indicate whether the function is one-to-one. - $B = \{ ( 4,2 ) , ( 5,2 ) , ( 6,8 ) , ( 7,4 ) \}$

Graph the two functions on one coordinate plane. - (x)= (x)=(x+5+7 $Graph the two functions on one coordinate plane. - \begin{array}{l} (x)=x^{3} \\ (x)=(x+5)^{3}+7 \end{array}$

Perform the requested operation on the given function. - $f ( x ) = 6 x - 7 , g ( x ) = 3 x - 5$ Find $( \mathrm { fg } ) ( \mathrm { x } )$ .

Find the composition. -If $f ( x ) = \sqrt { x + 9 }$ and $g ( x ) = 8 x - 13$ , find $f [ g ( x ) ]$

Evaluate the function. -If $f ( x ) = 5 x ^ { 2 } + 3 x - 4$ , find $f ( k - 1 )$

Graph the two functions on one coordinate plane. - $f ( x ) = \frac { 3 } { x }$ $g ( x ) = \frac { 3 } { x } + 4$ $Graph the two functions on one coordinate plane. - f ( x ) = \frac { 3 } { x } g ( x ) = \frac { 3 } { x } + 4$

Find the composition. -If $f ( x ) = x ^ { 2 } - 1$ and $h ( x ) = \sqrt { x + 7 }$ , find $( h \circ f ) ( - 3 )$

Perform the requested operation on the given function. - $f ( x ) = x + 3 , g ( x ) = x - 4$ Find $( f + g ) ( - 5 )$ .

Perform the requested operation on the given function. - $f ( x ) = x + 3 , g ( x ) = 5 x ^ { 2 } + 13 x + 6$ Find $( f g ) ( - 4 )$ .

Evaluate the function. -If $p ( x ) = 4 x ^ { 2 } + 3 x - 1$ , find $p \left( - \frac { a ^ { 2 } } { 4 } \right)$

Find the composition. -If $f ( x ) = x ^ { 2 } - 6$ and $h ( x ) = \sqrt { x + 13 }$ , find $( h \circ f ) ( - 4 )$

Evaluate the function. -If $f ( x ) = x ^ { 2 } - 2$ , find $f ( a - 3 )$ .

Find the composition. -If $f ( x ) = 6 x + 2$ and $g ( x ) = x + 4$ , find $( g \circ f ) ( x )$

Graph the two functions on one coordinate plane. - (x)=|x| y(x)=|x-4|+1 $Graph the two functions on one coordinate plane. - \begin{array}{l} (x)=|x| \\ y(x)=|x-4|+1 \end{array}$

Perform the requested operation on the given function. - $f ( x ) = 2 x ^ { 2 } - 7 x - 6 , g ( x ) = - 7 x + 2$ Find $( f + g ) ( - 4 )$ .