Question 1

Find an equation of variation for the given situation.
-m varies directly as p, and m = 20 when p = 5 .

Accepted Answer

A)   m=4 p 
B)   m=25 p 
C)  $\mathrm { m } = \frac { 1 } { 4 } \mathrm { p }$ 
D)  m=15 p 
A)   m=4 p 
B)   m=25 p 
C)  $\mathrm { m } = \frac { 1 } { 4 } \mathrm { p }$ 
D)  m=15 p

Question 2

For the pair of functions, find the indicated domain.
- f(x)=2 x-5 , $g ( x ) = \sqrt { x + 6 }$
Find the domain of $\mathrm { f } \circ \mathrm { g } \text {. }$

Accepted Answer

A)   (-6,6) 
B)  $[ - 6 , \infty )$ 
C)  $[ 0 , \infty )$ 
D)  $[ 6 , \infty )$ 
A)   (-6,6) 
B)  $[ - 6 , \infty )$ 
C)  $[ 0 , \infty )$ 
D)  $[ 6 , \infty )$

Question 3

The graph of the function f is shown below. Match the function g with the correct graph.
-g(x)= -f(-x)+ 4

Accepted Answer

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

Question 4

Determine if the graph is symmetric with respect to x-axis, y-axis, and/or the origin.
- 
A) y-axis
B) origin
C) x-axis
D) x-axis, origin

Accepted Answer

The answer of Determine if the graph is symmetric with...

Question 5

For the pair of functions, find the indicated sum, difference, product, or quotient.
-f(x)= 2x+5, g(x)= 6x+8
Find (fg)(x).

Accepted Answer

A)  $12 x ^ { 2 } + 40$ 
B)  $12 x ^ { 2 } + 46 x + 40$ 
C)  $12 x ^ { 2 } + 38 x + 40$ 
D)  $8 x ^ { 2 } + 46 x + 13$ 
A)  $12 x ^ { 2 } + 40$ 
B)  $12 x ^ { 2 } + 46 x + 40$ 
C)  $12 x ^ { 2 } + 38 x + 40$ 
D)  $8 x ^ { 2 } + 46 x + 13$

Question 6

Answer the question.
-How can the graph of $f ( x ) = - \frac { 1 } { x } + 6$ be obtained from the graph of $y = \frac { 1 } { x } ?$

Accepted Answer

A)  Reflect it across the  x -axis. Shift it 6 units up. 
B)  Reflect it across the y-axis. Shift it 6 units up. 
C)  Reflect it across the  x -axis. Shift it 6 units down. 
D)  Reflect it across the y-axis. Shift it 6 units down. 
A)  Reflect it across the  x -axis. Shift it 6 units up. 
B)  Reflect it across the y-axis. Shift it 6 units up. 
C)  Reflect it across the  x -axis. Shift it 6 units down. 
D)  Reflect it across the y-axis. Shift it 6 units down.

Question 7

Solve the problem.
-The weight of a body above the surface of the earth varies inversely as the square of its distance from the center of the earth. What is the effect on the weight when the distance is multiplied by 4 ?

Accepted Answer

A) The weight is divided by 4 . 
B) The weight is multiplied by 16 . 
C) The weight is multiplied by 4 . 
D) The weight is divided by 16 . 
A) The weight is divided by 4 . 
B) The weight is multiplied by 16 . 
C) The weight is multiplied by 4 . 
D) The weight is divided by 16 .

Question 8

For the pair of functions, find the indicated composition.
-$f ( x ) = x ^ { 4 } + 5 , g ( x ) = \sqrt [ 4 ] { x - 5 }$
Find $( g \circ f ) ( x )$

Accepted Answer

A)   x 
B)  $| x |$ 
C)  $x ^ { 4 }$ 
D)   -x 
A)   x 
B)  $| x |$ 
C)  $x ^ { 4 }$ 
D)   -x

Question 9

Determine algebraically whether the graph is symmetric with respect to the x-axis, the y-axis, and the origin.
-x4 + y4 = 10

Accepted Answer

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

Question 10

Solve the problem.
-The time it takes to complete a certain job varies inversely as the number of people working on that job. If it takes 36 hours for 11 carpenters to frame a house, then how long will it take 45 carpenters
To do the same job?

Accepted Answer

A) 40 hr 
B) 13.8 hr 
C) 45 hr 
D) 8.8 hr 
A) 40 hr 
B) 13.8 hr 
C) 45 hr 
D) 8.8 hr

Question 11

Write an equation for a function that has a graph with the given characteristics.
-The shape of $y = x ^ { 3 }$ is shifted  8.1  units to the right and then vertically shrunk by a factor of  0.4 .
A) $f ( x ) = 0.4 ( x - 8.1 ) ^ { 3 }$
B) $f ( x ) = 8.1 ( x - 0.4 ) ^ { 3 }$
C) $f ( x ) = 0.4 ( x + 8.1 ) ^ { 3 }$
D) $f ( x ) = 0.4 x ^ { 3 } + 8.1$

Accepted Answer

The answer of Write an equation for a function that...

Question 12

The graph of the function f is shown below. Match the function g with the correct graph.
-g(x)= f(x - 1)

Accepted Answer

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

Question 13

Given the graph of the function f(x   3x; find a formula for g(x) .
- 
A)  
в)  
C)  
D)

Accepted Answer

The answer of Given the graph of the function f(x...

Question 14

Determine if the graph is symmetric with respect to x-axis, y-axis, and/or the origin.
-

Accepted Answer

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

Question 15

Solve the problem.
-The gravitational attraction A between two masses varies inversely as the square of the distance between them. The force of attraction is 4 lb when the masses are 3 ft apart, what is the attraction When the masses are 6 ft apart?

Accepted Answer

A) 3 lb 
B) 1 lb 
C) 4 lb 
D) 2 lb 
A) 3 lb 
B) 1 lb 
C) 4 lb 
D) 2 lb

Question 16

For the pair of functions, find the indicated composition.
-$f ( x ) = \frac { 2 } { x } , g ( x ) = 7 x ^ { 4 }$
Find $( g \circ f ) ( x )$

Accepted Answer

A)  $\frac { 7 x ^ { 4 } } { 16 }$ 
B)  $\frac { 7 x ^ { 4 } } { 2 }$ 
C)  $\frac { 112 } { x ^ { 4 } }$ 
D)  $\frac { 2 } { 7 x ^ { 4 } }$ 
A)  $\frac { 7 x ^ { 4 } } { 16 }$ 
B)  $\frac { 7 x ^ { 4 } } { 2 }$ 
C)  $\frac { 112 } { x ^ { 4 } }$ 
D)  $\frac { 2 } { 7 x ^ { 4 } }$

Question 17

Solve.
-AAA Technology finds that the total revenue function associated with producing a new type of computer chip is $R ( x ) = 80 - 0.3 x ^ { 2 }$ and the total cost function is  C(x)=5 x+18 , where  x  represents the number of units of chips produced. Find the total profit function,  P(x) .

Accepted Answer

A)  $P ( x ) = 0.03 x ^ { 2 } + 5 x + 64$ 
B)  $P ( x ) = - 0.03 x ^ { 2 } + 5 x - 62$ 
C)  $P ( x ) = - 0.03 x ^ { 2 } - 5 x + 62$ 
D)  $P ( x ) = - 0.03 x ^ { 2 } + 5 x + 98$ 
A)  $P ( x ) = 0.03 x ^ { 2 } + 5 x + 64$ 
B)  $P ( x ) = - 0.03 x ^ { 2 } + 5 x - 62$ 
C)  $P ( x ) = - 0.03 x ^ { 2 } - 5 x + 62$ 
D)  $P ( x ) = - 0.03 x ^ { 2 } + 5 x + 98$

Question 18

For the function f, construct and simplify the difference quotient $\frac { f ( x + h ) - f ( x ) } { h }$
-$f ( x ) = \frac { 16 } { x + 14 }$

Accepted Answer

A)  $- \frac { 224 } { ( x + h + 14 ) ( x + 14 ) }$ 
B)  $- \frac { 16 } { ( x + h + 14 ) ( x + 14 ) }$ 
C)  $- \frac { 16 } { ( x + 16 ) ^ { 2 } }$ 
D)  $\frac { 16 } { ( x + h + 14 ) ( x + 14 ) }$ 
A)  $- \frac { 224 } { ( x + h + 14 ) ( x + 14 ) }$ 
B)  $- \frac { 16 } { ( x + h + 14 ) ( x + 14 ) }$ 
C)  $- \frac { 16 } { ( x + 16 ) ^ { 2 } }$ 
D)  $\frac { 16 } { ( x + h + 14 ) ( x + 14 ) }$

Question 19

Consider the functions F and G as shown in the graph. Provide an appropriate response.
-Graph G - F.

Accepted Answer

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

Question 20

Determine algebraically whether the graph is symmetric with respect to the x-axis, the y-axis, and the origin.
-$x ^ { 2 } + x y ^ { 2 } = - 4$

Accepted Answer

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

Find an equation of variation for the given situation. -m varies directly as p, and m = 20 when p = 5 .

For the pair of functions, find the indicated domain. - f(x)=2 x-5 , $g ( x ) = \sqrt { x + 6 }$ Find the domain of $\mathrm { f } \circ \mathrm { g } \text {. }$

The graph of the function f is shown below. Match the function g with the correct graph. -g(x)= -f(-x)+ 4

Determine if the graph is symmetric with respect to x-axis, y-axis, and/or the origin. - A) y-axis B) origin C) x-axis D) x-axis, origin

For the pair of functions, find the indicated sum, difference, product, or quotient. -f(x)= 2x+5, g(x)= 6x+8 Find (fg)(x).

Answer the question. -How can the graph of $f ( x ) = - \frac { 1 } { x } + 6$ be obtained from the graph of $y = \frac { 1 } { x } ?$

Solve the problem. -The weight of a body above the surface of the earth varies inversely as the square of its distance from the center of the earth. What is the effect on the weight when the distance is multiplied by 4 ?

For the pair of functions, find the indicated composition. - $f ( x ) = x ^ { 4 } + 5 , g ( x ) = \sqrt [ 4 ] { x - 5 }$ Find $( g \circ f ) ( x )$

Determine algebraically whether the graph is symmetric with respect to the x-axis, the y-axis, and the origin. -x4 + y4 = 10

Solve the problem. -The time it takes to complete a certain job varies inversely as the number of people working on that job. If it takes 36 hours for 11 carpenters to frame a house, then how long will it take 45 carpenters To do the same job?

The graph of the function f is shown below. Match the function g with the correct graph. -g(x)= f(x - 1)

Given the graph of the function f(x 3x; find a formula for g(x) . - A) в) C) D)

Determine if the graph is symmetric with respect to x-axis, y-axis, and/or the origin. -

Solve the problem. -The gravitational attraction A between two masses varies inversely as the square of the distance between them. The force of attraction is 4 lb when the masses are 3 ft apart, what is the attraction When the masses are 6 ft apart?

For the pair of functions, find the indicated composition. - $f ( x ) = \frac { 2 } { x } , g ( x ) = 7 x ^ { 4 }$ Find $( g \circ f ) ( x )$

Solve. -AAA Technology finds that the total revenue function associated with producing a new type of computer chip is $R ( x ) = 80 - 0.3 x ^ { 2 }$ and the total cost function is C(x)=5 x+18 , where x represents the number of units of chips produced. Find the total profit function, P(x) .

For the function f, construct and simplify the difference quotient $\frac { f ( x + h ) - f ( x ) } { h }$ - $f ( x ) = \frac { 16 } { x + 14 }$

Consider the functions F and G as shown in the graph. Provide an appropriate response. -Graph G - F.

Determine algebraically whether the graph is symmetric with respect to the x-axis, the y-axis, and the origin. - $x ^ { 2 } + x y ^ { 2 } = - 4$

Graphs, Functions, and Models

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Exam 2: More on Functions

Find an equation of variation for the given situation. -m varies directly as p, and m = 20 when p = 5 .

For the pair of functions, find the indicated domain. - f(x)=2 x-5 , g(x)=x+6g ( x ) = \sqrt { x + 6 }g(x)=x+6​ Find the domain of f∘g. \mathrm { f } \circ \mathrm { g } \text {. }f∘g.

The graph of the function f is shown below. Match the function g with the correct graph. -g(x)= -f(-x)+ 4

Determine if the graph is symmetric with respect to x-axis, y-axis, and/or the origin. - A) y-axis B) origin C) x-axis D) x-axis, origin

For the pair of functions, find the indicated sum, difference, product, or quotient. -f(x)= 2x+5, g(x)= 6x+8 Find (fg)(x).

Answer the question. -How can the graph of f(x)=−1x+6f ( x ) = - \frac { 1 } { x } + 6f(x)=−x1​+6 be obtained from the graph of y=1x?y = \frac { 1 } { x } ?y=x1​?

Solve the problem. -The weight of a body above the surface of the earth varies inversely as the square of its distance from the center of the earth. What is the effect on the weight when the distance is multiplied by 4 ?

For the pair of functions, find the indicated composition. - f(x)=x4+5,g(x)=x−54f ( x ) = x ^ { 4 } + 5 , g ( x ) = \sqrt [ 4 ] { x - 5 }f(x)=x4+5,g(x)=4x−5​ Find (g∘f)(x)( g \circ f ) ( x )(g∘f)(x)

Determine algebraically whether the graph is symmetric with respect to the x-axis, the y-axis, and the origin. -x4 + y4 = 10

Solve the problem. -The time it takes to complete a certain job varies inversely as the number of people working on that job. If it takes 36 hours for 11 carpenters to frame a house, then how long will it take 45 carpenters To do the same job?

The graph of the function f is shown below. Match the function g with the correct graph. -g(x)= f(x - 1)

Given the graph of the function f(x 3x; find a formula for g(x) . - A) в) C) D)

Determine if the graph is symmetric with respect to x-axis, y-axis, and/or the origin. -

Solve the problem. -The gravitational attraction A between two masses varies inversely as the square of the distance between them. The force of attraction is 4 lb when the masses are 3 ft apart, what is the attraction When the masses are 6 ft apart?

For the pair of functions, find the indicated composition. - f(x)=2x,g(x)=7x4f ( x ) = \frac { 2 } { x } , g ( x ) = 7 x ^ { 4 }f(x)=x2​,g(x)=7x4 Find (g∘f)(x)( g \circ f ) ( x )(g∘f)(x)

For the function f, construct and simplify the difference quotient f(x+h)−f(x)h\frac { f ( x + h ) - f ( x ) } { h }hf(x+h)−f(x)​ - f(x)=16x+14f ( x ) = \frac { 16 } { x + 14 }f(x)=x+1416​

Consider the functions F and G as shown in the graph. Provide an appropriate response. -Graph G - F.

Determine algebraically whether the graph is symmetric with respect to the x-axis, the y-axis, and the origin. - x2+xy2=−4x ^ { 2 } + x y ^ { 2 } = - 4x2+xy2=−4

Graphs, Functions, and Models

Quadratic Functions and Equations; Inequalities

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Exponential and Logarithmic Functions

Systems of Equations and Matrices

Conic Sections

Sequences, Series, and Combinatorics

Filters

For the pair of functions, find the indicated domain. - f(x)=2 x-5 , $g ( x ) = \sqrt { x + 6 }$ Find the domain of $\mathrm { f } \circ \mathrm { g } \text {. }$

Answer the question. -How can the graph of $f ( x ) = - \frac { 1 } { x } + 6$ be obtained from the graph of $y = \frac { 1 } { x } ?$

For the pair of functions, find the indicated composition. - $f ( x ) = x ^ { 4 } + 5 , g ( x ) = \sqrt [ 4 ] { x - 5 }$ Find $( g \circ f ) ( x )$

For the pair of functions, find the indicated composition. - $f ( x ) = \frac { 2 } { x } , g ( x ) = 7 x ^ { 4 }$ Find $( g \circ f ) ( x )$

For the function f, construct and simplify the difference quotient $\frac { f ( x + h ) - f ( x ) } { h }$ - $f ( x ) = \frac { 16 } { x + 14 }$

Determine algebraically whether the graph is symmetric with respect to the x-axis, the y-axis, and the origin. - $x ^ { 2 } + x y ^ { 2 } = - 4$