Question 1

The graph of $y = \sqrt { x }$ is shifted 4 units to the left. Then the graph is shifted 9 units upward.

Accepted Answer

A)  $y = \sqrt { x + 9 } + 4$ 
B)  $y = 9 \sqrt { x + 4 }$ 
C)  $y = \sqrt { x + 4 } + 9$ 
D)  $y = \sqrt { x - 4 } + 9$ 
A)  $y = \sqrt { x + 9 } + 4$ 
B)  $y = 9 \sqrt { x + 4 }$ 
C)  $y = \sqrt { x + 4 } + 9$ 
D)  $y = \sqrt { x - 4 } + 9$

Question 2

Assume that from 1930 to 1980 , the number of deaths from lead poisoning (per 100,000 people) decreased dramatically and could be modeled by $\mathrm { f } ( \mathrm { x } ) = - 0.0148 \mathrm { x } ^ { 2 } + 54.2 \mathrm { x } - 49,200$, where $\mathrm { x }$ is the year. Determine when, to the nearest year, this death rate was 150 or less by graphing $\mathrm { y } = \mathrm { f } ( \mathrm { x } )$ and $\mathrm { y } = 150$ in $[ 1930,1980,10 ]$ by $[ 0,200$, 25 ].

Accepted Answer

A)  1960 or after 
B)  1973 or after 
C)  1964 or after 
D)  1967 or after 
A)  1960 or after 
B)  1973 or after 
C)  1964 or after 
D)  1967 or after

Question 3

Find the inverse of the function.
-$$f ( x ) = \frac { x } { 3 } - 6$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = x + 9$ 
B)  $f ^ { - 1 } ( x ) = 3 x + 6$ 
C)  $f ^ { - 1 } ( x ) = 3 x - 18$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = 3 \mathrm { x } + 18$ 
A)  $f ^ { - 1 } ( x ) = x + 9$ 
B)  $f ^ { - 1 } ( x ) = 3 x + 6$ 
C)  $f ^ { - 1 } ( x ) = 3 x - 18$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = 3 \mathrm { x } + 18$

Question 4

The graphs of two functions f(x) and g(x) are given.
-Solve $f ( x ) \geq g ( x )$.

Accepted Answer

A)  $- 3 \leq x \leq 3$ 
B)  $x \leq - 3$ or $x \geq 3$ 
C)  $x \leq - 2$ or $x \geq 2$ 
D)  $- 2 \leq x \leq 2$ 
A)  $- 3 \leq x \leq 3$ 
B)  $x \leq - 3$ or $x \geq 3$ 
C)  $x \leq - 2$ or $x \geq 2$ 
D)  $- 2 \leq x \leq 2$

Question 5

Determine whether (f(g(x)) $$( f ( g ( x ) ) = x \text { and whether } ( g ( f ( x ) ) = x$$
-$f ( x ) = \sqrt [ 5 ] { x - 7 } , g ( x ) = x ^ { 5 } + 7$

Accepted Answer

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

Question 6

The surface area of a sphere is $f ( x ) = 4 \pi x ^ { 2 }$ square inches, where  x  is the radius of the sphere in inches. Find the inverse of this function.

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

Sketch the graph of the pair of functions. Use a dashed line for g(x)
-$$f ( x ) = | x | , g ( x ) = \frac { 1 } { 2 } | x + 6 | - 3$$

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin.
-$y = - 5 x ^ { 3 }$

Accepted Answer

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

Question 11

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 12

Assume that the profit P made when  t  units are sold, $t > 0$, is given by $P ( t ) = t ^ { 2 } - 18 t + 72$ For what values of  t  will there be a profit (that is, $\mathrm { P } > 0 )$?

Accepted Answer

A)   t=18 
B)  $6  12$ 
A)   t=18 
B)  $6  12$

Question 13

Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin.
-y = | 4 x | + 2

Accepted Answer

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

Question 14

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.
-$$f ( x ) = \frac { 5 } { x }$$

Accepted Answer

A) 
  
B) 
  
C) 
$\text { Function is its own inverse }$
  
D) 
 
 Function is its own inverse 
A) 
  
B) 
  
C) 
$\text { Function is its own inverse }$
  
D) 
 
 Function is its own inverse

Question 15

Determine whether or not the function is one-to-one.
-f(x) = 0.43

Accepted Answer

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

Question 16

Solve the equation
-$\sqrt { x + 7 } + 5 = x$

Accepted Answer

A)   x=2,9 
B)   x=9,18 
C)   x=2 
D)   x=9 
A)   x=2,9 
B)   x=9,18 
C)   x=2 
D)   x=9

Question 17

Determine the values of x for which f(x) and g(x) are inverse functions.
-$$f ( x ) = x ^ { 2 } - 13 , g ( x ) = - \sqrt { x + 13 }$$

Accepted Answer

A)  $x \geq 13$ 
B)  $x \leq 13$ 
C)  $x \leq 0$ 
D)  $x \geq 0$ 
A)  $x \geq 13$ 
B)  $x \leq 13$ 
C)  $x \leq 0$ 
D)  $x \geq 0$

Question 18

Solve the equation
-$2 x ^ { 1 / 2 } - 3 x ^ { 1 / 4 } - 2 = 0$

Accepted Answer

A)  16 
B)   -2,-1 
C)   2,- $\frac { 1 } { 2 }$ 
D)   16,$\frac { 1 } { 16 }$ 
A)  16 
B)   -2,-1 
C)   2,- $\frac { 1 } { 2 }$ 
D)   16,$\frac { 1 } { 16 }$

Question 19

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

Accepted Answer

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

Question 20

The function defined by  f(x)=x+2  was used to encode the following message:
15 3 22 10 9 7 16 11 23 21
using the alphabet coding method  (A=1, B=2, C=3, ...) . Find the inverse and decode the message.

Accepted Answer

The answer of The function defined by  f(x)=x+2 ...

The graph of $y = \sqrt { x }$ is shifted 4 units to the left. Then the graph is shifted 9 units upward.

Find the inverse of the function. - $f ( x ) = \frac { x } { 3 } - 6$

The graphs of two functions f(x) and g(x) are given. -Solve $f ( x ) \geq g ( x )$ . $The graphs of two functions f(x) and g(x) are given. -Solve f ( x ) \geq g ( x ) .$

Determine whether (f(g(x)) $( f ( g ( x ) ) = x \text { and whether } ( g ( f ( x ) ) = x$ - $f ( x ) = \sqrt [ 5 ] { x - 7 } , g ( x ) = x ^ { 5 } + 7$

The surface area of a sphere is $f ( x ) = 4 \pi x ^ { 2 }$ square inches, where x is the radius of the sphere in inches. Find the inverse of this function.

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

Sketch the graph of the pair of functions. Use a dashed line for g(x) - $f ( x ) = | x | , g ( x ) = \frac { 1 } { 2 } | x + 6 | - 3$ $Sketch the graph of the pair of functions. Use a dashed line for g(x) - f ( x ) = | x | , g ( x ) = \frac { 1 } { 2 } | x + 6 | - 3$

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

Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. - $y = - 5 x ^ { 3 }$

Assume that the profit P made when t units are sold, $t > 0$ , is given by $P ( t ) = t ^ { 2 } - 18 t + 72$ For what values of t will there be a profit (that is, $\mathrm { P } > 0 )$ ?

Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. -y = | 4 x | + 2

Determine whether or not the function is one-to-one. -f(x) = 0.43

Solve the equation - $\sqrt { x + 7 } + 5 = x$

Determine the values of x for which f(x) and g(x) are inverse functions. - $f ( x ) = x ^ { 2 } - 13 , g ( x ) = - \sqrt { x + 13 }$

Solve the equation - $2 x ^ { 1 / 2 } - 3 x ^ { 1 / 4 } - 2 = 0$

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

The function defined by f(x)=x+2 was used to encode the following message: 15 3 22 10 9 7 16 11 23 21 using the alphabet coding method (A=1, B=2, C=3, ...) . Find the inverse and decode the message.

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

The graph of y=xy = \sqrt { x }y=x​ is shifted 4 units to the left. Then the graph is shifted 9 units upward.

Find the inverse of the function. - f(x)=x3−6f ( x ) = \frac { x } { 3 } - 6f(x)=3x​−6

The graphs of two functions f(x) and g(x) are given. -Solve f(x)≥g(x)f ( x ) \geq g ( x )f(x)≥g(x) .

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−75,g(x)=x5+7f ( x ) = \sqrt [ 5 ] { x - 7 } , g ( x ) = x ^ { 5 } + 7f(x)=5x−7​,g(x)=x5+7

The surface area of a sphere is f(x)=4πx2f ( x ) = 4 \pi x ^ { 2 }f(x)=4πx2 square inches, where x is the radius of the sphere in inches. Find the inverse of this function.

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

Sketch the graph of the pair of functions. Use a dashed line for g(x) - f(x)=∣x∣,g(x)=12∣x+6∣−3f ( x ) = | x | , g ( x ) = \frac { 1 } { 2 } | x + 6 | - 3f(x)=∣x∣,g(x)=21​∣x+6∣−3

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

Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. - y=−5x3y = - 5 x ^ { 3 }y=−5x3

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. -

Assume that the profit P made when t units are sold, t>0t > 0t>0 , is given by P(t)=t2−18t+72P ( t ) = t ^ { 2 } - 18 t + 72P(t)=t2−18t+72 For what values of t will there be a profit (that is, P>0)\mathrm { P } > 0 )P>0) ?

Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. -y = | 4 x | + 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. - f(x)=5xf ( x ) = \frac { 5 } { x }f(x)=x5​

Determine whether or not the function is one-to-one. -f(x) = 0.43

Solve the equation - x+7+5=x\sqrt { x + 7 } + 5 = xx+7​+5=x

Determine the values of x for which f(x) and g(x) are inverse functions. - f(x)=x2−13,g(x)=−x+13f ( x ) = x ^ { 2 } - 13 , g ( x ) = - \sqrt { x + 13 }f(x)=x2−13,g(x)=−x+13​

Solve the equation - 2x1/2−3x1/4−2=02 x ^ { 1 / 2 } - 3 x ^ { 1 / 4 } - 2 = 02x1/2−3x1/4−2=0

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

The function defined by f(x)=x+2 was used to encode the following message: 15 3 22 10 9 7 16 11 23 21 using the alphabet coding method (A=1, B=2, C=3, ...) . Find the inverse and decode the message.

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

The graph of $y = \sqrt { x }$ is shifted 4 units to the left. Then the graph is shifted 9 units upward.

Find the inverse of the function. - $f ( x ) = \frac { x } { 3 } - 6$

The graphs of two functions f(x) and g(x) are given. -Solve $f ( x ) \geq g ( x )$ . $The graphs of two functions f(x) and g(x) are given. -Solve f ( x ) \geq g ( x ) .$

Determine whether (f(g(x)) $( f ( g ( x ) ) = x \text { and whether } ( g ( f ( x ) ) = x$ - $f ( x ) = \sqrt [ 5 ] { x - 7 } , g ( x ) = x ^ { 5 } + 7$

The surface area of a sphere is $f ( x ) = 4 \pi x ^ { 2 }$ square inches, where x is the radius of the sphere in inches. Find the inverse of this function.

Sketch the graph of the pair of functions. Use a dashed line for g(x) - $f ( x ) = | x | , g ( x ) = \frac { 1 } { 2 } | x + 6 | - 3$ $Sketch the graph of the pair of functions. Use a dashed line for g(x) - f ( x ) = | x | , g ( x ) = \frac { 1 } { 2 } | x + 6 | - 3$

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

Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. - $y = - 5 x ^ { 3 }$

Assume that the profit P made when t units are sold, $t > 0$ , is given by $P ( t ) = t ^ { 2 } - 18 t + 72$ For what values of t will there be a profit (that is, $\mathrm { P } > 0 )$ ?

Solve the equation - $\sqrt { x + 7 } + 5 = x$

Determine the values of x for which f(x) and g(x) are inverse functions. - $f ( x ) = x ^ { 2 } - 13 , g ( x ) = - \sqrt { x + 13 }$

Solve the equation - $2 x ^ { 1 / 2 } - 3 x ^ { 1 / 4 } - 2 = 0$