Question 1

Determine if the complete graph represents a function that is even, odd, or neither.
-

Accepted Answer

A)  odd 
B)  neither 
C)  even 
A)  odd 
B)  neither 
C)  even

Question 2

Solve the equation
-$\sqrt [ 3 ] { x + 8 } = 2$

Accepted Answer

A)   x=-6 
B)   x=8 
C)   x=0 
D)   x=-4 
A)   x=-6 
B)   x=8 
C)   x=0 
D)   x=-4

Question 3

A balloon in the shape of a sphere is deflating. Given that t represents the time, in minutes, since it began losing air, the radius of the balloon (in cm) is r(t)=23- t . Let the equation $V ( r ) = \frac { 4 } { 3 } \pi r ^ { 3 }$ represent the volume of a sphere of radius  r . Find and interpret $( \mathrm { V } \circ \mathrm { r } ) ( \mathrm { t } )$

Accepted Answer

A)  $( \mathrm { V } \circ \circ \mathrm { r } ) ( \mathrm { t } ) = 23 - \frac { 4 } { 3 } \pi ( 23 - \mathrm { t } ) ^ { 3 }$ ; This is the volume of the air lost by the balloon (in cm3) as a function of time (in minutes). 
B)  $( \mathrm { V } \circ \mathrm { r } ) ( \mathrm { t } ) = \frac { 4 } { 3 } \pi ( 23 - \mathrm { t } ) ^ { 3 }$ ; This is the volume of the air lost by the balloon (in cm3) as a function of time (in minutes). 
C)  $( V \circ r ) ( t ) = \frac { 4 } { 3 } \pi ( 23 - t ) ^ { 3 }$ ; This is the volume of the balloon (in  cm3 ) as a function of time (in minutes). 
D)  $( \mathrm { V } \circ \mathrm { r } ) ( \mathrm { t } ) = \frac { 4 } { 3 } \pi ( \mathrm { t } - 23 ) ^ { 3 }$ ; This is the volume of the balloon (in  cm3 ) as a function of time (in minutes). 
A)  $( \mathrm { V } \circ \circ \mathrm { r } ) ( \mathrm { t } ) = 23 - \frac { 4 } { 3 } \pi ( 23 - \mathrm { t } ) ^ { 3 }$ ; This is the volume of the air lost by the balloon (in cm3) as a function of time (in minutes). 
B)  $( \mathrm { V } \circ \mathrm { r } ) ( \mathrm { t } ) = \frac { 4 } { 3 } \pi ( 23 - \mathrm { t } ) ^ { 3 }$ ; This is the volume of the air lost by the balloon (in cm3) as a function of time (in minutes). 
C)  $( V \circ r ) ( t ) = \frac { 4 } { 3 } \pi ( 23 - t ) ^ { 3 }$ ; This is the volume of the balloon (in  cm3 ) as a function of time (in minutes). 
D)  $( \mathrm { V } \circ \mathrm { r } ) ( \mathrm { t } ) = \frac { 4 } { 3 } \pi ( \mathrm { t } - 23 ) ^ { 3 }$ ; This is the volume of the balloon (in  cm3 ) as a function of time (in minutes).

Question 4

Sketch the graph of the pair of functions. Use a dashed line for g(x)
-$f(x)=\sqrt[3]{x}, g(x)=\sqrt[3]{-x}+4$

Accepted Answer

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

Question 5

Use the given graph of f(x) $f ( x ) = a x ^ { 2 } + b x + c$ c to solve the specified inequality.
-$\mathrm{f}(\mathrm{x})<0$

Accepted Answer

A)  $x < 6$ 
B)  $x < 0$ 
C)  all real numbers 
D)  no solution 
A)  $x < 6$ 
B)  $x < 0$ 
C)  all real numbers 
D)  no solution

Question 6

Determine whether (f(g(x)) $$( f ( g ( x ) ) = x \text { and whether } ( g ( f ( x ) ) = x$$
-$f ( x ) = \sqrt { x + 1 } , g ( x ) = x ^ { 2 }$

Accepted Answer

A)  No, yes 
B)  Yes, yes 
C)  No, no 
D)  Yes, no 
A)  No, yes 
B)  Yes, yes 
C)  No, no 
D)  Yes, no

Question 7

Determine if the function f defined by the arrow diagram has an inverse. If it does, create an arrow diagram that defines
the inverse. If not, explain why not.
-

Accepted Answer

A)  Yes; 
B)  No; the function is not one-to-one
  
A)  Yes; 
B)  No; the function is not one-to-one

Question 8

Determine whether the function is even, odd, or neither.
-$f ( x ) = - 9 x ^ { 3 } + 6 x$

Accepted Answer

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

Question 9

Solve the inequality by using algebraic and graphical methods. Round to three decimal places, if necessary.
-$$| 5 x + 9 | < 2$$

Accepted Answer

A)  $- \frac { 11 } { 5 }  - \frac { 7 } { 5 }$ 
D)  $x < - \frac { 11 } { 5 }$ 
A)  $- \frac { 11 } { 5 }  - \frac { 7 } { 5 }$ 
D)  $x < - \frac { 11 } { 5 }$

Question 10

Graph the given function as a solid line (or curve) and its inverse as a dashed line (or curve) on the same set of axes.
-$(x)=-7 x+4$

Accepted Answer

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

Question 11

Sketch the graph of the pair of functions. Use a dashed line for g(x)
-$f(x)=x^{2}, g(x)=x^{2}-6$

Accepted Answer

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

Question 12

Provide an appropriate response.
-If f(x) represents the percent of college students in the United States who own a laptop computer and g(x) represents the number of college students in the United States, with x equal to the number of years from 2010,
Then what function represents the number of college students in the United States with laptop computers, with x
Equal to the number of years from 2010?

Accepted Answer

A)  $( f \circ g ) ( x )$ 
B)  $( g \circ f ) ( x )$ 
C)  $( f + g ) ( x )$ 
D)  $( f \cdot g ) ( x )$ 
A)  $( f \circ g ) ( x )$ 
B)  $( g \circ f ) ( x )$ 
C)  $( f + g ) ( x )$ 
D)  $( f \cdot g ) ( x )$

Question 13

Find the requested function value.
-Find $( g \circ f ) ( \quad )$ when $f ( x ) = x + 9$ and $g ( x ) = x ^ { 2 } + 5 x - 6$

Accepted Answer

A)  363 
B)  501 
C)  12,357 
D)  1323 
A)  363 
B)  501 
C)  12,357 
D)  1323

Question 14

Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin.
-$x ^ { 2 } + y ^ { 2 } = 9$

Accepted Answer

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

Question 15

Decide whether or not the functions are inverses of each other.
-$f ( x ) = 5 x - 5 , \quad g ( x ) = \frac { 1 } { 5 } x + 1$

Accepted Answer

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

Question 16

For the pair of functions, perform the indicated operation.
-$f ( x ) = \sqrt { 2 x + 5 } , g ( x ) = \sqrt { 25 x - 16 } \quad$ Find $( f \cdot g ) ( x )$

Accepted Answer

A)  $( 2 x + 5 ) ( 5 x - 4 )$ 
B)  $( \sqrt { 2 x + 5 } ) ( \sqrt { 25 x - 16 } )$ 
C)  $( 2 x + 5 ) ( 25 x - 16 )$ 
D)  $( 5 x - 4 ) ( \sqrt { 2 x + 5 } )$ 
A)  $( 2 x + 5 ) ( 5 x - 4 )$ 
B)  $( \sqrt { 2 x + 5 } ) ( \sqrt { 25 x - 16 } )$ 
C)  $( 2 x + 5 ) ( 25 x - 16 )$ 
D)  $( 5 x - 4 ) ( \sqrt { 2 x + 5 } )$

Question 17

Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin.
- y= $\frac { 3 } { x }$

Accepted Answer

A)   x -axis,  y -axis, origin 
B)  Origin 
C)   y -axis 
D)  No symmetry 
A)   x -axis,  y -axis, origin 
B)  Origin 
C)   y -axis 
D)  No symmetry

Question 18

Solve the inequality.
-$64 - x ^ { 2 } \geq 0$

Accepted Answer

A)  $x \leq 8$ 
B)  $- 8 \leq x \leq 8$ 
C)  $x \leq - 8 \text { or } x \geq 8$ 
D)  $x \leq - 32 \text { or } x \geq 32$ 
A)  $x \leq 8$ 
B)  $- 8 \leq x \leq 8$ 
C)  $x \leq - 8 \text { or } x \geq 8$ 
D)  $x \leq - 32 \text { or } x \geq 32$

Question 19

Find the requested composition of functions.
-Given $f ( x ) = - 5 x + 9$ and $g ( x ) = 3 x + 2$, find $( g \circ f ) ( x )$

Accepted Answer

A)  $- 15 x + 19$ 
B)  $- 15 x + 29$ 
C)  $15 x + 29$ 
D)  $- 15 x - 25$ 
A)  $- 15 x + 19$ 
B)  $- 15 x + 29$ 
C)  $15 x + 29$ 
D)  $- 15 x - 25$

Question 20

Years ago, people used fountain pens. The ink was very "wet" and so a blotter was used to absorb "wet" ink left
on the surface of the paper. Suppose you have a single sheet of graph paper and that you have just used your
fountain pen to graph the one-to-one function f. Explain how, if the ink is "wet", you could now obtain the
graph of f $\mathrm { f } ^ { - 1 }$ using only your sheet of graph paper. (Hint: Fold the sheet of graph paper.)

Accepted Answer

With the graph facing up, fold

Determine if the complete graph represents a function that is even, odd, or neither. -

Solve the equation - $\sqrt [ 3 ] { x + 8 } = 2$

Sketch the graph of the pair of functions. Use a dashed line for g(x) - $f(x)=\sqrt[3]{x}, g(x)=\sqrt[3]{-x}+4$ $Sketch the graph of the pair of functions. Use a dashed line for g(x) - f(x)=\sqrt[3]{x}, g(x)=\sqrt[3]{-x}+4$

Use the given graph of f(x) $f ( x ) = a x ^ { 2 } + b x + c$ c to solve the specified inequality. - $\mathrm{f}(\mathrm{x})<0$ $Use the given graph of f(x) f ( x ) = a x ^ { 2 } + b x + c c to solve the specified inequality. - \mathrm{f}(\mathrm{x})<0$

Determine whether (f(g(x)) $( f ( g ( x ) ) = x \text { and whether } ( g ( f ( x ) ) = x$ - $f ( x ) = \sqrt { x + 1 } , g ( x ) = x ^ { 2 }$

Determine if the function f defined by the arrow diagram has an inverse. If it does, create an arrow diagram that defines the inverse. If not, explain why not. -

Determine whether the function is even, odd, or neither. - $f ( x ) = - 9 x ^ { 3 } + 6 x$

Solve the inequality by using algebraic and graphical methods. Round to three decimal places, if necessary. - $| 5 x + 9 | < 2$

Graph the given function as a solid line (or curve) and its inverse as a dashed line (or curve) on the same set of axes. - $(x)=-7 x+4$

Sketch the graph of the pair of functions. Use a dashed line for g(x) - $f(x)=x^{2}, g(x)=x^{2}-6$ $Sketch the graph of the pair of functions. Use a dashed line for g(x) - f(x)=x^{2}, g(x)=x^{2}-6$

Find the requested function value. -Find $( g \circ f ) ( \quad )$ when $f ( x ) = x + 9$ and $g ( x ) = x ^ { 2 } + 5 x - 6$

Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. - $x ^ { 2 } + y ^ { 2 } = 9$

Decide whether or not the functions are inverses of each other. - $f ( x ) = 5 x - 5 , \quad g ( x ) = \frac { 1 } { 5 } x + 1$

For the pair of functions, perform the indicated operation. - $f ( x ) = \sqrt { 2 x + 5 } , g ( x ) = \sqrt { 25 x - 16 } \quad$ Find $( f \cdot g ) ( x )$

Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. - y= $\frac { 3 } { x }$

Solve the inequality. - $64 - x ^ { 2 } \geq 0$

Find the requested composition of functions. -Given $f ( x ) = - 5 x + 9$ and $g ( x ) = 3 x + 2$ , find $( g \circ f ) ( x )$

Functions, Graphs, and Models; Linear Functions

Linear Models, Equations, and Inequalities

Quadratic, Piecewise-Defined, and Power Functions

Exponential and Logarithmic Functions

Higher-Degree Polynomial and Rational Functions

Systems of Equations and Matrices

Special Topics in Algebra

Filters

Exam 4: Additional Topics With Functions

Determine if the complete graph represents a function that is even, odd, or neither. -

Solve the equation - x+83=2\sqrt [ 3 ] { x + 8 } = 23x+8​=2

Sketch the graph of the pair of functions. Use a dashed line for g(x) - f(x)=x3,g(x)=−x3+4f(x)=\sqrt[3]{x}, g(x)=\sqrt[3]{-x}+4f(x)=3x​,g(x)=3−x​+4

Use the given graph of f(x) f(x)=ax2+bx+cf ( x ) = a x ^ { 2 } + b x + cf(x)=ax2+bx+c c to solve the specified inequality. - f(x)<0\mathrm{f}(\mathrm{x})<0f(x)<0

Determine whether (f(g(x)) (f(g(x))=x and whether (g(f(x))=x( f ( g ( x ) ) = x \text { and whether } ( g ( f ( x ) ) = x(f(g(x))=x and whether (g(f(x))=x - f(x)=x+1,g(x)=x2f ( x ) = \sqrt { x + 1 } , g ( x ) = x ^ { 2 }f(x)=x+1​,g(x)=x2

Determine if the function f defined by the arrow diagram has an inverse. If it does, create an arrow diagram that defines the inverse. If not, explain why not. -

Determine whether the function is even, odd, or neither. - f(x)=−9x3+6xf ( x ) = - 9 x ^ { 3 } + 6 xf(x)=−9x3+6x

Solve the inequality by using algebraic and graphical methods. Round to three decimal places, if necessary. - ∣5x+9∣<2| 5 x + 9 | < 2∣5x+9∣<2

Graph the given function as a solid line (or curve) and its inverse as a dashed line (or curve) on the same set of axes. - (x)=−7x+4(x)=-7 x+4(x)=−7x+4

Sketch the graph of the pair of functions. Use a dashed line for g(x) - f(x)=x2,g(x)=x2−6f(x)=x^{2}, g(x)=x^{2}-6f(x)=x2,g(x)=x2−6

Find the requested function value. -Find (g∘f)()( g \circ f ) ( \quad )(g∘f)() when f(x)=x+9f ( x ) = x + 9f(x)=x+9 and g(x)=x2+5x−6g ( x ) = x ^ { 2 } + 5 x - 6g(x)=x2+5x−6

Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. - x2+y2=9x ^ { 2 } + y ^ { 2 } = 9x2+y2=9

Decide whether or not the functions are inverses of each other. - f(x)=5x−5,g(x)=15x+1f ( x ) = 5 x - 5 , \quad g ( x ) = \frac { 1 } { 5 } x + 1f(x)=5x−5,g(x)=51​x+1

For the pair of functions, perform the indicated operation. - f(x)=2x+5,g(x)=25x−16f ( x ) = \sqrt { 2 x + 5 } , g ( x ) = \sqrt { 25 x - 16 } \quadf(x)=2x+5​,g(x)=25x−16​ Find (f⋅g)(x)( f \cdot g ) ( x )(f⋅g)(x)

Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. - y= 3x\frac { 3 } { x }x3​

Solve the inequality. - 64−x2≥064 - x ^ { 2 } \geq 064−x2≥0

Find the requested composition of functions. -Given f(x)=−5x+9f ( x ) = - 5 x + 9f(x)=−5x+9 and g(x)=3x+2g ( x ) = 3 x + 2g(x)=3x+2 , find (g∘f)(x)( g \circ f ) ( x )(g∘f)(x)

Functions, Graphs, and Models; Linear Functions

Linear Models, Equations, and Inequalities

Quadratic, Piecewise-Defined, and Power Functions

Exponential and Logarithmic Functions

Higher-Degree Polynomial and Rational Functions

Systems of Equations and Matrices

Special Topics in Algebra

Filters

Solve the equation - $\sqrt [ 3 ] { x + 8 } = 2$

Sketch the graph of the pair of functions. Use a dashed line for g(x) - $f(x)=\sqrt[3]{x}, g(x)=\sqrt[3]{-x}+4$ $Sketch the graph of the pair of functions. Use a dashed line for g(x) - f(x)=\sqrt[3]{x}, g(x)=\sqrt[3]{-x}+4$

Use the given graph of f(x) $f ( x ) = a x ^ { 2 } + b x + c$ c to solve the specified inequality. - $\mathrm{f}(\mathrm{x})<0$ $Use the given graph of f(x) f ( x ) = a x ^ { 2 } + b x + c c to solve the specified inequality. - \mathrm{f}(\mathrm{x})<0$

Determine whether (f(g(x)) $( f ( g ( x ) ) = x \text { and whether } ( g ( f ( x ) ) = x$ - $f ( x ) = \sqrt { x + 1 } , g ( x ) = x ^ { 2 }$

Determine whether the function is even, odd, or neither. - $f ( x ) = - 9 x ^ { 3 } + 6 x$

Solve the inequality by using algebraic and graphical methods. Round to three decimal places, if necessary. - $| 5 x + 9 | < 2$

Graph the given function as a solid line (or curve) and its inverse as a dashed line (or curve) on the same set of axes. - $(x)=-7 x+4$

Sketch the graph of the pair of functions. Use a dashed line for g(x) - $f(x)=x^{2}, g(x)=x^{2}-6$ $Sketch the graph of the pair of functions. Use a dashed line for g(x) - f(x)=x^{2}, g(x)=x^{2}-6$

Find the requested function value. -Find $( g \circ f ) ( \quad )$ when $f ( x ) = x + 9$ and $g ( x ) = x ^ { 2 } + 5 x - 6$

Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. - $x ^ { 2 } + y ^ { 2 } = 9$

Decide whether or not the functions are inverses of each other. - $f ( x ) = 5 x - 5 , \quad g ( x ) = \frac { 1 } { 5 } x + 1$

For the pair of functions, perform the indicated operation. - $f ( x ) = \sqrt { 2 x + 5 } , g ( x ) = \sqrt { 25 x - 16 } \quad$ Find $( f \cdot g ) ( x )$

Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. - y= $\frac { 3 } { x }$

Solve the inequality. - $64 - x ^ { 2 } \geq 0$

Find the requested composition of functions. -Given $f ( x ) = - 5 x + 9$ and $g ( x ) = 3 x + 2$ , find $( g \circ f ) ( x )$