Question 1

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

Accepted Answer

A)  $x ^ { 4 } - 18 x ^ { 2 } + 72$ 
B)  $x ^ { 4 } - 18 x ^ { 2 } + 90$ 
C)  $x ^ { 4 } + 18 x ^ { 2 } + 72$ 
D)  $x ^ { 4 } + 18 x ^ { 2 } + 90$ 
A)  $x ^ { 4 } - 18 x ^ { 2 } + 72$ 
B)  $x ^ { 4 } - 18 x ^ { 2 } + 90$ 
C)  $x ^ { 4 } + 18 x ^ { 2 } + 72$ 
D)  $x ^ { 4 } + 18 x ^ { 2 } + 90$

Question 2

Solve the problem.
-The number of dislocated electric impulses per cubic inch in a transformer increases when lightning strikes by $\mathrm { D } ( \mathrm { x } ) = 4700 ( 5 ) ^ { \mathrm { x } }$, where $\mathrm { x }$ is the time in milliseconds of the lightning strike. Find the number of dislocated impulses at $x = 0$ and $x = 3$.

Accepted Answer

A)  $4700 ; 14,687,500$ 
B)  $4700 ; 70,500$ 
C)  $4700 ; 587,500$ 
D)  23,$500 ; 587,500$ 
A)  $4700 ; 14,687,500$ 
B)  $4700 ; 70,500$ 
C)  $4700 ; 587,500$ 
D)  23,$500 ; 587,500$

Question 3

Graph the function as a solid curve and its inverse as a dashed curve.
-$f(x)=\frac{5}{4} x+6$

Accepted Answer

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

Question 4

Find the inverse of the relation.
-{(10, -3), (-4, 20), (12, -20)}

Accepted Answer

A) {(-3, 10), (20, -4), (-20, 12)} 
B) {(10, 20), (10, -4), (-20, 12)} 
C) {(-3, 10), (12, -4), (-20, 20)} 
A) {(-3, 10), (20, -4), (-20, 12)} 
B) {(10, 20), (10, -4), (-20, 12)} 
C) {(-3, 10), (12, -4), (-20, 20)}

Question 5

Graph.
-$x=\left(\frac{1}{2}\right)^{y}$

Accepted Answer

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

Question 6

Graph the equation of the relation using a solid line, and then graph the inverse of the relation using a dashed line.
-y = 6 + 5x

Accepted Answer

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

Question 7

Graph the relation using solid circles and the inverse using open circles.
-{(2, 8), (-2, -8), (2, -6), (-2, 6)}

Accepted Answer

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

Question 8

Solve the problem.
-A size 6 dress in Country $C$ is size 36 in Country D. A function that converts dress sizes in Country C to those in Country $D$ is $f ( x ) = x + 30$. Find a formula for the inverse of the function described.

Accepted Answer

A)  $f ^ { - 1 } ( x ) = x + 30$ 
B)  $f ^ { - 1 } ( x ) = x - 30$ 
C)  $f ^ { - 1 } ( x ) = \frac { x } { - 30 }$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { 30 }$ 
A)  $f ^ { - 1 } ( x ) = x + 30$ 
B)  $f ^ { - 1 } ( x ) = x - 30$ 
C)  $f ^ { - 1 } ( x ) = \frac { x } { - 30 }$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { 30 }$

Question 9

Graph.
-$f(x)=\left(\frac{1}{4}\right)^{x}+3$

Accepted Answer

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

Question 10

Solve the problem.
-An accountant tabulated a firm's profits for four recent years in the following table: 
 
The accountant then fit both a linear graph and an exponential curve (seen below) to the data, in order to estimate future profits. Use the exponential graph to estimate the profits in the year $2001 .$

Accepted Answer

A)  About $\$ 1,300,000$ 
B)  About $\$ 300,000$ 
C)  About $\$ 1,000,000$ 
D)  About $\$ 750,000$ 
A)  About $\$ 1,300,000$ 
B)  About $\$ 300,000$ 
C)  About $\$ 1,000,000$ 
D)  About $\$ 750,000$

Question 11

Find f(x) and g(x) such that h(x) = $(f \circ g)(x)$.
-$$h ( x ) = \frac { 1 } { x ^ { 2 } } + 6$$

Accepted Answer

A)  $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = 6$ 
B)  $f ( x ) = \frac { 1 } { x } , g ( x ) = \frac { 1 } { x } + 6$ 
C)  $f ( x ) = x , g ( x ) = \frac { 1 } { x } + 6$ 
D)  $f ( x ) = x + 6 , g ( x ) = \frac { 1 } { x ^ { 2 } }$ 
A)  $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = 6$ 
B)  $f ( x ) = \frac { 1 } { x } , g ( x ) = \frac { 1 } { x } + 6$ 
C)  $f ( x ) = x , g ( x ) = \frac { 1 } { x } + 6$ 
D)  $f ( x ) = x + 6 , g ( x ) = \frac { 1 } { x ^ { 2 } }$

Question 12

Graph the relation using solid circles and the inverse using open circles.
-{(10, -5), (8, -4), (6, -3), (4, -2)}

Accepted Answer

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

Question 13

Graph.
-$$f ( x ) = 3 ^ { x } - 2$$

Accepted Answer

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

Question 14

Graph.
-$f(x)= 3^{x}$

Accepted Answer

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

Question 15

Graph the equation of the relation using a solid line, and then graph the inverse of the relation using a dashed line.
-y = 8x - 6

Accepted Answer

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

Question 16

Find the inverse of the relation.
-{(2, 9), (-2, -9), (4, -7), (-4, 7)}

Accepted Answer

A) {(9, 2), (-9, -2), (-7, -2), (7, -4)} 
B) {(9, 2), (2, -2), (-7, 4), (7, -4)} 
C) {(9, 2), (-9, -2), (-7, 4), (7, -4)} 
A) {(9, 2), (-9, -2), (-7, -2), (7, -4)} 
B) {(9, 2), (2, -2), (-7, 4), (7, -4)} 
C) {(9, 2), (-9, -2), (-7, 4), (7, -4)}

Question 17

Determine whether the given function is one-to-one. If so, find a formula for the inverse.
-$$f ( x ) = \frac { 3 x + 8 } { - 6 x - 2 }$$

Accepted Answer

A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 3 \mathrm { x } + 8 } { - 6 \mathrm { x } - 2 }$ 
B)  $f ^ { - 1 } ( x ) = \frac { 2 x + 8 } { - 6 x - 3 }$ 
C)  Not a one-to-one function 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { - 6 \mathrm { x } - 3 } { 2 \mathrm { x } + 8 }$ 
A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 3 \mathrm { x } + 8 } { - 6 \mathrm { x } - 2 }$ 
B)  $f ^ { - 1 } ( x ) = \frac { 2 x + 8 } { - 6 x - 3 }$ 
C)  Not a one-to-one function 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { - 6 \mathrm { x } - 3 } { 2 \mathrm { x } + 8 }$

Question 18

Find the requested composition of functions.
-Given $f ( x ) = 4 x + 9$ and $g ( x ) = 2 x - 1$, find $f \circ g ( x )$.

Accepted Answer

A)  $8 x + 8$ 
B)  $8 x + 5$ 
C)  $8 x + 17$ 
D)  $8 x + 13$ 
A)  $8 x + 8$ 
B)  $8 x + 5$ 
C)  $8 x + 17$ 
D)  $8 x + 13$

Question 19

Graph.
-$f(x)=3^{-x}$

Accepted Answer

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

Question 20

Use composition to verify whether or not the inverse is correct.
-$$f ( x ) = 6 x - 4 , f ^ { - 1 } ( x ) = \frac { x + 6 } { 4 }$$

Accepted Answer

A) True 
 B)False

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

Graph the function as a solid curve and its inverse as a dashed curve. - $f(x)=\frac{5}{4} x+6$ $Graph the function as a solid curve and its inverse as a dashed curve. - f(x)=\frac{5}{4} x+6$

Find the inverse of the relation. -{(10, -3), (-4, 20), (12, -20)}

Graph. - $x=\left(\frac{1}{2}\right)^{y}$ $Graph. - x=\left(\frac{1}{2}\right)^{y}$

Graph the equation of the relation using a solid line, and then graph the inverse of the relation using a dashed line. -y = 6 + 5x

Graph the relation using solid circles and the inverse using open circles. -{(2, 8), (-2, -8), (2, -6), (-2, 6)}

Solve the problem. -A size 6 dress in Country $C$ is size 36 in Country D. A function that converts dress sizes in Country C to those in Country $D$ is $f ( x ) = x + 30$ . Find a formula for the inverse of the function described.

Graph. - $f(x)=\left(\frac{1}{4}\right)^{x}+3$ $Graph. - f(x)=\left(\frac{1}{4}\right)^{x}+3$

Find f(x) and g(x) such that h(x) = $(f \circ g)(x)$ . - $h ( x ) = \frac { 1 } { x ^ { 2 } } + 6$

Graph the relation using solid circles and the inverse using open circles. -{(10, -5), (8, -4), (6, -3), (4, -2)}

Graph. - $f ( x ) = 3 ^ { x } - 2$ $Graph. - f ( x ) = 3 ^ { x } - 2$

Graph. - $f(x)= 3^{x}$ $Graph. - f(x)= 3^{x}$

Graph the equation of the relation using a solid line, and then graph the inverse of the relation using a dashed line. -y = 8x - 6

Find the inverse of the relation. -{(2, 9), (-2, -9), (4, -7), (-4, 7)}

Determine whether the given function is one-to-one. If so, find a formula for the inverse. - $f ( x ) = \frac { 3 x + 8 } { - 6 x - 2 }$

Find the requested composition of functions. -Given $f ( x ) = 4 x + 9$ and $g ( x ) = 2 x - 1$ , find $f \circ g ( x )$ .

Graph. - $f(x)=3^{-x}$ $Graph. - f(x)=3^{-x}$

Use composition to verify whether or not the inverse is correct. - $f ( x ) = 6 x - 4 , f ^ { - 1 } ( x ) = \frac { x + 6 } { 4 }$

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Operations

Polynomials: Factoring

Rational Expressions and Equations

Graphs, Functions, and Applications

Systems of Equations

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Exam 12: Exponential Functions and Logarithmic Functions

Find the requested composition of functions. -Given f(x)=x2+9f ( x ) = x ^ { 2 } + 9f(x)=x2+9 and g(x)=x2−9g ( x ) = x ^ { 2 } - 9g(x)=x2−9 , find f∘g(x)f \circ g ( x )f∘g(x) .

Graph the function as a solid curve and its inverse as a dashed curve. - f(x)=54x+6f(x)=\frac{5}{4} x+6f(x)=45​x+6

Find the inverse of the relation. -{(10, -3), (-4, 20), (12, -20)}

Graph. - x=(12)yx=\left(\frac{1}{2}\right)^{y}x=(21​)y

Graph the equation of the relation using a solid line, and then graph the inverse of the relation using a dashed line. -y = 6 + 5x

Graph the relation using solid circles and the inverse using open circles. -{(2, 8), (-2, -8), (2, -6), (-2, 6)}

Solve the problem. -A size 6 dress in Country CCC is size 36 in Country D. A function that converts dress sizes in Country C to those in Country DDD is f(x)=x+30f ( x ) = x + 30f(x)=x+30 . Find a formula for the inverse of the function described.

Graph. - f(x)=(14)x+3f(x)=\left(\frac{1}{4}\right)^{x}+3f(x)=(41​)x+3

Find f(x) and g(x) such that h(x) = (f∘g)(x)(f \circ g)(x)(f∘g)(x) . - h(x)=1x2+6h ( x ) = \frac { 1 } { x ^ { 2 } } + 6h(x)=x21​+6

Graph the relation using solid circles and the inverse using open circles. -{(10, -5), (8, -4), (6, -3), (4, -2)}

Graph. - f(x)=3x−2f ( x ) = 3 ^ { x } - 2f(x)=3x−2

Graph. - f(x)=3xf(x)= 3^{x}f(x)=3x

Graph the equation of the relation using a solid line, and then graph the inverse of the relation using a dashed line. -y = 8x - 6

Find the inverse of the relation. -{(2, 9), (-2, -9), (4, -7), (-4, 7)}

Determine whether the given function is one-to-one. If so, find a formula for the inverse. - f(x)=3x+8−6x−2f ( x ) = \frac { 3 x + 8 } { - 6 x - 2 }f(x)=−6x−23x+8​

Find the requested composition of functions. -Given f(x)=4x+9f ( x ) = 4 x + 9f(x)=4x+9 and g(x)=2x−1g ( x ) = 2 x - 1g(x)=2x−1 , find f∘g(x)f \circ g ( x )f∘g(x) .

Graph. - f(x)=3−xf(x)=3^{-x}f(x)=3−x

Use composition to verify whether or not the inverse is correct. - f(x)=6x−4,f−1(x)=x+64f ( x ) = 6 x - 4 , f ^ { - 1 } ( x ) = \frac { x + 6 } { 4 }f(x)=6x−4,f−1(x)=4x+6​

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Operations

Polynomials: Factoring

Rational Expressions and Equations

Graphs, Functions, and Applications

Systems of Equations

More on Inequalities

Radical Expressions, Equations, and Functions

Quadratic Equations and Functions

Filters

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

Graph the function as a solid curve and its inverse as a dashed curve. - $f(x)=\frac{5}{4} x+6$ $Graph the function as a solid curve and its inverse as a dashed curve. - f(x)=\frac{5}{4} x+6$

Graph. - $x=\left(\frac{1}{2}\right)^{y}$ $Graph. - x=\left(\frac{1}{2}\right)^{y}$

Solve the problem. -A size 6 dress in Country $C$ is size 36 in Country D. A function that converts dress sizes in Country C to those in Country $D$ is $f ( x ) = x + 30$ . Find a formula for the inverse of the function described.

Graph. - $f(x)=\left(\frac{1}{4}\right)^{x}+3$ $Graph. - f(x)=\left(\frac{1}{4}\right)^{x}+3$

Find f(x) and g(x) such that h(x) = $(f \circ g)(x)$ . - $h ( x ) = \frac { 1 } { x ^ { 2 } } + 6$

Graph. - $f ( x ) = 3 ^ { x } - 2$ $Graph. - f ( x ) = 3 ^ { x } - 2$

Graph. - $f(x)= 3^{x}$ $Graph. - f(x)= 3^{x}$

Determine whether the given function is one-to-one. If so, find a formula for the inverse. - $f ( x ) = \frac { 3 x + 8 } { - 6 x - 2 }$

Find the requested composition of functions. -Given $f ( x ) = 4 x + 9$ and $g ( x ) = 2 x - 1$ , find $f \circ g ( x )$ .

Graph. - $f(x)=3^{-x}$ $Graph. - f(x)=3^{-x}$

Use composition to verify whether or not the inverse is correct. - $f ( x ) = 6 x - 4 , f ^ { - 1 } ( x ) = \frac { x + 6 } { 4 }$