Question 1

Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin.
-$y = 0.79 x ^ { 2 } + | x | + 7$

Accepted Answer

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

Question 2

The graph of the function y $y = f ( x ) \text { is given. On the same axes, sketch the graph of } f ^ { - 1 } ( x )$ . Use a dashed line for the inverse
function.
-A size 4 dress in Country C is size 42 in Country D. A function that converts dress sizes in Country $C$ to those in Country $D$ is $f ( x ) = x + 38$. Find a formula for the inverse of this function.

Accepted Answer

A)  $f ^ { - 1 } ( x ) = x + 38$ 
B)  $f ^ { - 1 } ( x ) = \frac { x } { - 38 }$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { 38 }$ 
D)  $f ^ { - 1 } ( x ) = x - 38$ 
A)  $f ^ { - 1 } ( x ) = x + 38$ 
B)  $f ^ { - 1 } ( x ) = \frac { x } { - 38 }$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { 38 }$ 
D)  $f ^ { - 1 } ( x ) = x - 38$

Question 3

Find the inverse of the function.
-$$f ( x ) = - 5 - 3 x$$

Accepted Answer

A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = - \frac { 5 } { 3 } + \frac { \mathrm { x } } { 3 }$ 
B)  $f ^ { - 1 } ( x ) = \frac { 5 } { 3 } - \frac { x } { 3 }$ 
C)  $f ^ { - 1 } ( x ) = - \frac { 5 } { 3 } - \frac { x } { 3 }$ 
D)  $f ^ { - 1 } ( x ) = - 2 - x$ 
A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = - \frac { 5 } { 3 } + \frac { \mathrm { x } } { 3 }$ 
B)  $f ^ { - 1 } ( x ) = \frac { 5 } { 3 } - \frac { x } { 3 }$ 
C)  $f ^ { - 1 } ( x ) = - \frac { 5 } { 3 } - \frac { x } { 3 }$ 
D)  $f ^ { - 1 } ( x ) = - 2 - x$

Question 4

Solve the equation
-$( x + 3 ) ^ { 3 / 2 } = 27$

Accepted Answer

A)   x=14 
B)   x=9 
C)   x=6 
D)   x=12 
A)   x=14 
B)   x=9 
C)   x=6 
D)   x=12

Question 5

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.
-$$f ( x ) = - 5 x$$

Accepted Answer

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

Question 6

Determine whether or not the function is one-to-one.
-

Accepted Answer

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

Question 7

The graph of the function y $y = f ( x ) \text { is given. On the same axes, sketch the graph of } f ^ { - 1 } ( x )$ . Use a dashed line for the inverse
function.
-

Accepted Answer

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

Question 8

Decide whether or not the functions are inverses of each other.
-$f ( x ) = - \frac { 2 } { 7 } x , \quad g ( x ) = - \frac { 7 } { 2 } x$

Accepted Answer

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

Question 9

The graph of $y = \sqrt { x }$ is shifted 4 units to the right.

Accepted Answer

A)  $y = \sqrt { x - 4 }$ 
B)  $y = \sqrt { x } + 4$ 
C)  $y = \sqrt { x + 4 }$ 
D)  $y = \sqrt { x } - 4$ 
A)  $y = \sqrt { x - 4 }$ 
B)  $y = \sqrt { x } + 4$ 
C)  $y = \sqrt { x + 4 }$ 
D)  $y = \sqrt { x } - 4$

Question 10

Solve the inequality by using algebraic and graphical methods. Round to three decimal places, if necessary.
-$| x - 8 | \leq 9$

Accepted Answer

A)  $x \leq - 1$ or $x \geq 17$ 
B)  $- 17 \leq x \leq 1$ 
C)  $- 1 \leq x \leq 17$ 
D)  $- 9 \leq x \leq 9$ 
A)  $x \leq - 1$ or $x \geq 17$ 
B)  $- 17 \leq x \leq 1$ 
C)  $- 1 \leq x \leq 17$ 
D)  $- 9 \leq x \leq 9$

Question 11

Sketch the graph of the pair of functions. Use a dashed line for g(x)
-$$f ( x ) = x ^ { 2 } , g ( x ) = - \frac { 1 } { 4 } ( x + 3 ) ^ { 2 } + 4$$

Accepted Answer

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

Question 12

For the pair of functions, perform the indicated operation.
-$f ( x ) = 7 x ^ { 2 } - 8 x , g ( x ) = x ^ { 2 } - 2 x - 48 \quad$ Find $\left( \frac { f } { g } \right) ( x )$

Accepted Answer

A)  $\frac { 7 x - 8 } { - 2 }$ 
B)  $\frac { 7 x ^ { 2 } - 8 x } { x ^ { 2 } - 2 x - 48 }$ 
C)  $\frac { 7 - \mathrm { x } } { 48 }$ 
D)  $\frac { 7 x } { x + 1 }$ 
A)  $\frac { 7 x - 8 } { - 2 }$ 
B)  $\frac { 7 x ^ { 2 } - 8 x } { x ^ { 2 } - 2 x - 48 }$ 
C)  $\frac { 7 - \mathrm { x } } { 48 }$ 
D)  $\frac { 7 x } { x + 1 }$

Question 13

The volume of a cylinder whose height is equal to twice its radius is $\mathrm { f } ( \mathrm { x } ) = 2 \pi \mathrm { x } ^ { 3 } \mathrm {~cm} ^ { 3 }$ , where  x  is the radius of the cylinder in  cm . Find the inverse of this function.

Accepted Answer

A)  $f ^ { - 1 } ( x ) = 2 \pi \sqrt [ 3 ] { x }$ 
B)  $f ^ { - 1 } ( x ) = \frac { 1 } { 2 \pi x ^ { 3 } }$ 
C)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { \frac { x } { 2 \pi } }$ 
D)  $f ^ { - 1 } ( x ) = \frac { \sqrt [ 3 ] { x } } { 2 \pi }$ 
A)  $f ^ { - 1 } ( x ) = 2 \pi \sqrt [ 3 ] { x }$ 
B)  $f ^ { - 1 } ( x ) = \frac { 1 } { 2 \pi x ^ { 3 } }$ 
C)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { \frac { x } { 2 \pi } }$ 
D)  $f ^ { - 1 } ( x ) = \frac { \sqrt [ 3 ] { x } } { 2 \pi }$

Question 14

Find the specified domain and express it in interval notation.
-If f(x)=2x+10  and g(x)=x2+3 , evaluate $\left( \frac { g } { f } \right)  { ( 2 ) }$.

Accepted Answer

A)  $\frac { 1 } { 2 }$ 
B)  2 
C)  98 
D)  21 
A)  $\frac { 1 } { 2 }$ 
B)  2 
C)  98 
D)  21

Question 15

Use the quadratic formula or graphing methods to
-$$4 x ^ { 2 } + 20 x + 8 \geq 0$$

Accepted Answer

A)  $x \geq \frac { - 5 + \sqrt { 17 } } { 2 } \approx - 0.438$ 
B)  $\frac { - 5 - \sqrt { 17 } } { 2 } \approx - 4.562 \leq x \leq \frac { - 5 + \sqrt { 17 } } { 2 } \approx - 0.438$ 
C)  $x \leq \frac { - 5 - \sqrt { 17 } } { 2 } \approx - 4.562$ 
D)  $x \leq \frac { - 5 - \sqrt { 17 } } { 2 } \approx - 4.562$ or $x \geq \frac { - 5 + \sqrt { 17 } } { 2 } \approx - 0.438$ 
A)  $x \geq \frac { - 5 + \sqrt { 17 } } { 2 } \approx - 0.438$ 
B)  $\frac { - 5 - \sqrt { 17 } } { 2 } \approx - 4.562 \leq x \leq \frac { - 5 + \sqrt { 17 } } { 2 } \approx - 0.438$ 
C)  $x \leq \frac { - 5 - \sqrt { 17 } } { 2 } \approx - 4.562$ 
D)  $x \leq \frac { - 5 - \sqrt { 17 } } { 2 } \approx - 4.562$ or $x \geq \frac { - 5 + \sqrt { 17 } } { 2 } \approx - 0.438$

Question 16

Find the specified domain and express it in interval notation.
-If  f(x)=3 x+4  and  g(x)=x-x2 , evaluate  (f+g)(3) .

Accepted Answer

A)  6 
B)  19 
C)  7 
D)   -78 
A)  6 
B)  19 
C)  7 
D)   -78

Question 17

Aretailer that n games can be sold in a month at a price of 20-0.1n dollars per game. Assume that he buys each game for $13, and sells every one that he buys. if he whishes to make a profit of at least $100 per month on sales of this game, how many games must he sell each month?

Accepted Answer

A)  $$0 \leq n \leq 20$$ 
B)  $$20 \leq n \leq 50$$ 
C)  $$20 \leq n \leq 70$$ 
D)  $$25 \leq n \leq 35$$ 
A)  $$0 \leq n \leq 20$$ 
B)  $$20 \leq n \leq 50$$ 
C)  $$20 \leq n \leq 70$$ 
D)  $$25 \leq n \leq 35$$

Question 18

Sketch the graph of the pair of functions. Use a dashed line for g(x)
-$$f ( x ) = x ^ { 2 } , g ( x ) = \frac { 1 } { 5 } x ^ { 2 }$$

Accepted Answer

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

Question 19

Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin.
-$y = - 5 x ^ { 2 } - 1$

Accepted Answer

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

Question 20

Use the quadratic formula or graphing methods to
-$$6 x ^ { 2 } - 27 x + 6 \geq 0$$

Accepted Answer

A)  $x \geq \frac { 9 + \sqrt { 65 } } { 4 } \approx 4.266$ 
B)  $\frac { 9 - \sqrt { 65 } } { 4 } \approx 0.234 \leq x \leq \frac { 9 + \sqrt { 65 } } { 4 } \approx 4.266$ 
C)  $x \leq \frac { 9 - \sqrt { 65 } } { 4 } \approx 0.234$ 
D)  $x \leq \frac { 9 - \sqrt { 65 } } { 4 } \approx 0.234$ or $x \geq \frac { 9 + \sqrt { 65 } } { 4 } \approx 4.266$ 
A)  $x \geq \frac { 9 + \sqrt { 65 } } { 4 } \approx 4.266$ 
B)  $\frac { 9 - \sqrt { 65 } } { 4 } \approx 0.234 \leq x \leq \frac { 9 + \sqrt { 65 } } { 4 } \approx 4.266$ 
C)  $x \leq \frac { 9 - \sqrt { 65 } } { 4 } \approx 0.234$ 
D)  $x \leq \frac { 9 - \sqrt { 65 } } { 4 } \approx 0.234$ or $x \geq \frac { 9 + \sqrt { 65 } } { 4 } \approx 4.266$

Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. - $y = 0.79 x ^ { 2 } + | x | + 7$

Find the inverse of the function. - $f ( x ) = - 5 - 3 x$

Solve the equation - $( x + 3 ) ^ { 3 / 2 } = 27$

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. - $f ( x ) = - 5 x$

Determine whether or not the function is one-to-one. -

Decide whether or not the functions are inverses of each other. - $f ( x ) = - \frac { 2 } { 7 } x , \quad g ( x ) = - \frac { 7 } { 2 } x$

The graph of $y = \sqrt { x }$ is shifted 4 units to the right.

Solve the inequality by using algebraic and graphical methods. Round to three decimal places, if necessary. - $| x - 8 | \leq 9$

Sketch the graph of the pair of functions. Use a dashed line for g(x) - $f ( x ) = x ^ { 2 } , g ( x ) = - \frac { 1 } { 4 } ( x + 3 ) ^ { 2 } + 4$ $Sketch the graph of the pair of functions. Use a dashed line for g(x) - f ( x ) = x ^ { 2 } , g ( x ) = - \frac { 1 } { 4 } ( x + 3 ) ^ { 2 } + 4$

For the pair of functions, perform the indicated operation. - $f ( x ) = 7 x ^ { 2 } - 8 x , g ( x ) = x ^ { 2 } - 2 x - 48 \quad$ Find $\left( \frac { f } { g } \right) ( x )$

The volume of a cylinder whose height is equal to twice its radius is $\mathrm { f } ( \mathrm { x } ) = 2 \pi \mathrm { x } ^ { 3 } \mathrm {~cm} ^ { 3 }$ , where x is the radius of the cylinder in cm . Find the inverse of this function.

Find the specified domain and express it in interval notation. -If f(x)=2x+10 and g(x)=x²+3 , evaluate $\left( \frac { g } { f } \right) { ( 2 ) }$ .

Use the quadratic formula or graphing methods to - $4 x ^ { 2 } + 20 x + 8 \geq 0$

Find the specified domain and express it in interval notation. -If f(x)=3 x+4 and g(x)=x-x² , evaluate (f+g)(3) .

Aretailer that n games can be sold in a month at a price of 20-0.1n dollars per game. Assume that he buys each game for $13, and sells every one that he buys. if he whishes to make a profit of at least $100 per month on sales of this game, how many games must he sell each month?

Sketch the graph of the pair of functions. Use a dashed line for g(x) - $f ( x ) = x ^ { 2 } , g ( x ) = \frac { 1 } { 5 } x ^ { 2 }$ $Sketch the graph of the pair of functions. Use a dashed line for g(x) - f ( x ) = x ^ { 2 } , g ( x ) = \frac { 1 } { 5 } x ^ { 2 }$

Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. - $y = - 5 x ^ { 2 } - 1$

Use the quadratic formula or graphing methods to - $6 x ^ { 2 } - 27 x + 6 \geq 0$

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 whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. - y=0.79x2+∣x∣+7y = 0.79 x ^ { 2 } + | x | + 7y=0.79x2+∣x∣+7

Find the inverse of the function. - f(x)=−5−3xf ( x ) = - 5 - 3 xf(x)=−5−3x

Solve the equation - (x+3)3/2=27( x + 3 ) ^ { 3 / 2 } = 27(x+3)3/2=27

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. - f(x)=−5xf ( x ) = - 5 xf(x)=−5x

Determine whether or not the function is one-to-one. -

The graph of the function y y=f(x) is given. On the same axes, sketch the graph of f−1(x)y = f ( x ) \text { is given. On the same axes, sketch the graph of } f ^ { - 1 } ( x )y=f(x) is given. On the same axes, sketch the graph of f−1(x) . Use a dashed line for the inverse function. -

Decide whether or not the functions are inverses of each other. - f(x)=−27x,g(x)=−72xf ( x ) = - \frac { 2 } { 7 } x , \quad g ( x ) = - \frac { 7 } { 2 } xf(x)=−72​x,g(x)=−27​x

The graph of y=xy = \sqrt { x }y=x​ is shifted 4 units to the right.

Solve the inequality by using algebraic and graphical methods. Round to three decimal places, if necessary. - ∣x−8∣≤9| x - 8 | \leq 9∣x−8∣≤9

Sketch the graph of the pair of functions. Use a dashed line for g(x) - f(x)=x2,g(x)=−14(x+3)2+4f ( x ) = x ^ { 2 } , g ( x ) = - \frac { 1 } { 4 } ( x + 3 ) ^ { 2 } + 4f(x)=x2,g(x)=−41​(x+3)2+4

For the pair of functions, perform the indicated operation. - f(x)=7x2−8x,g(x)=x2−2x−48f ( x ) = 7 x ^ { 2 } - 8 x , g ( x ) = x ^ { 2 } - 2 x - 48 \quadf(x)=7x2−8x,g(x)=x2−2x−48 Find (fg)(x)\left( \frac { f } { g } \right) ( x )(gf​)(x)

The volume of a cylinder whose height is equal to twice its radius is f(x)=2πx3 cm3\mathrm { f } ( \mathrm { x } ) = 2 \pi \mathrm { x } ^ { 3 } \mathrm {~cm} ^ { 3 }f(x)=2πx3 cm3 , where x is the radius of the cylinder in cm . Find the inverse of this function.

Find the specified domain and express it in interval notation. -If f(x)=2x+10 and g(x)=x2+3 , evaluate (gf)(2)\left( \frac { g } { f } \right) { ( 2 ) }(fg​)(2) .

Use the quadratic formula or graphing methods to - 4x2+20x+8≥04 x ^ { 2 } + 20 x + 8 \geq 04x2+20x+8≥0

Find the specified domain and express it in interval notation. -If f(x)=3 x+4 and g(x)=x-x2 , evaluate (f+g)(3) .

Aretailer that n games can be sold in a month at a price of 20-0.1n dollars per game. Assume that he buys each game for $13, and sells every one that he buys. if he whishes to make a profit of at least $100 per month on sales of this game, how many games must he sell each month?

Sketch the graph of the pair of functions. Use a dashed line for g(x) - f(x)=x2,g(x)=15x2f ( x ) = x ^ { 2 } , g ( x ) = \frac { 1 } { 5 } x ^ { 2 }f(x)=x2,g(x)=51​x2

Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. - y=−5x2−1y = - 5 x ^ { 2 } - 1y=−5x2−1

Use the quadratic formula or graphing methods to - 6x2−27x+6≥06 x ^ { 2 } - 27 x + 6 \geq 06x2−27x+6≥0

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

Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. - $y = 0.79 x ^ { 2 } + | x | + 7$

Find the inverse of the function. - $f ( x ) = - 5 - 3 x$

Solve the equation - $( x + 3 ) ^ { 3 / 2 } = 27$

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. - $f ( x ) = - 5 x$

Decide whether or not the functions are inverses of each other. - $f ( x ) = - \frac { 2 } { 7 } x , \quad g ( x ) = - \frac { 7 } { 2 } x$

The graph of $y = \sqrt { x }$ is shifted 4 units to the right.

Solve the inequality by using algebraic and graphical methods. Round to three decimal places, if necessary. - $| x - 8 | \leq 9$

Sketch the graph of the pair of functions. Use a dashed line for g(x) - $f ( x ) = x ^ { 2 } , g ( x ) = - \frac { 1 } { 4 } ( x + 3 ) ^ { 2 } + 4$ $Sketch the graph of the pair of functions. Use a dashed line for g(x) - f ( x ) = x ^ { 2 } , g ( x ) = - \frac { 1 } { 4 } ( x + 3 ) ^ { 2 } + 4$

For the pair of functions, perform the indicated operation. - $f ( x ) = 7 x ^ { 2 } - 8 x , g ( x ) = x ^ { 2 } - 2 x - 48 \quad$ Find $\left( \frac { f } { g } \right) ( x )$

The volume of a cylinder whose height is equal to twice its radius is $\mathrm { f } ( \mathrm { x } ) = 2 \pi \mathrm { x } ^ { 3 } \mathrm {~cm} ^ { 3 }$ , where x is the radius of the cylinder in cm . Find the inverse of this function.

Find the specified domain and express it in interval notation. -If f(x)=2x+10 and g(x)=x²+3 , evaluate $\left( \frac { g } { f } \right) { ( 2 ) }$ .

Use the quadratic formula or graphing methods to - $4 x ^ { 2 } + 20 x + 8 \geq 0$

Find the specified domain and express it in interval notation. -If f(x)=3 x+4 and g(x)=x-x² , evaluate (f+g)(3) .

Sketch the graph of the pair of functions. Use a dashed line for g(x) - $f ( x ) = x ^ { 2 } , g ( x ) = \frac { 1 } { 5 } x ^ { 2 }$ $Sketch the graph of the pair of functions. Use a dashed line for g(x) - f ( x ) = x ^ { 2 } , g ( x ) = \frac { 1 } { 5 } x ^ { 2 }$

Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. - $y = - 5 x ^ { 2 } - 1$

Use the quadratic formula or graphing methods to - $6 x ^ { 2 } - 27 x + 6 \geq 0$