AnswersAlgebraic ReasoningAnalyzing Compositions of Functions

Analyzing Compositions of Functions — Quiz Answers

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1
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If f of x is equal to 3 x and g of x is equal to 2 x , what is open paren g circ f close paren times x ?

A
open paren g circ f close paren times x is equal to 6 x
B
open paren g circ f close paren times x is equal to 5 x squared
C
open paren g circ f close paren times x is equal to 5 x
D
open paren g circ f close paren times x is equal to 6 x squared
2
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If f of x is equal to x plus 4 and g of x is equal to x squared minus 1 , what is open paren g circ f close paren times x ?

A
open paren g circ f close paren times x is equal to x squared plus 8 x plus 15
B
open paren g circ f close paren times x is equal to x squared plus 3
C
open paren g circ f close paren times x is equal to x squared plus 8 x plus 16
D
open paren g circ f close paren times x is equal to x squared minus 1
3

If f of x is equal to x plus 7 and g of x is equal to 1 over x , what is open paren f circ g close paren times x ?

A
open paren f circ g close paren times x is equal to x plus 7 plus 1 over x
B
open paren f circ g close paren times x is equal to the fraction with numerator 1 and denominator x plus 7
C
open paren f circ g close paren times x is equal to 1 over x plus 7
D
open paren f circ g close paren times x is equal to 1 plus 7 over x
4

If f of x is equal to 1 over x and g of x is equal to x minus 2 , which of the following is the graph of open paren f circ g close paren times x ?

A
Image with description On a coordinate plane, the scale on the x axis range from negative 5 to 5 in increments of 1, and the scale on the y axis range from negative 7 to 3 in increments of 1. The graph is made up of two different curves that do not meet. One of the curves opens up to the right in quadrants 1 and 5 and passes through the point (1 comma negative 3). The curve crosses the x axis at nonsignificant numbers. The other curve opens down and to the left in quadrant 3 and passes through the point (negative 1 comma negative 3).
B
Image with description On a coordinate plane, the scale on the x axis range from negative 7 to 2 in increments of 1, and the scale on the y axis range from negative 5 to 5 in increments of 1. The graph is made up of two different curves that do not meet. One of the curves opens up and to the right in quadrants 1 and 2 and passes through the point (negative 1 comma 1). The curve crosses the x axis at nonsignificant numbers. The other curve opens down and to the left in quadrant 3 and passes through the point (negative 3 comma negative 1).
C
Image with description On a coordinate plane, the x and y axes list from negative 5 to 5 in increments of 1. The graph is made up of two different curves that do not meet. One of the curves opens up and to the right in quadrant 1 and passes through the point (1 comma 1). The other curve opens down and to the left in quadrant 3 and passes through the point (negative 1 comma negative 1).
D
Image with description On a coordinate plane, the scale on the x axis range from negative 3 to 7 in increments of 1, and the scale on the y axis range from negative 5 to 5 in increments of 1. The graph is made up of two different curves that do not meet. One of the curves opens up to the right in quadrant 1 and passes through the point (3 comma 1). The other curve opens down and to the left in quadrants 3 and 4 and passes through the point (1 comma negative 1). The curve crosses the y axis at nonsignificant numbers.
5

If f of x is equal to the fraction with numerator x minus 1 and denominator 3 and g of x is equal to 3 x plus 1 , what is open paren f circ g close paren times x ?

A
open paren f circ g close paren times x is equal to 3 x
B
open paren f circ g close paren times x is equal to x
C
open paren f circ g close paren times x is equal to x minus 3
D
open paren f circ g close paren times x is equal to 3 x plus 1
6

If f of x is equal to x and g of x is equal to 2 , what is open paren f circ g close paren times x ?

A
open paren f circ g close paren times x is equal to 2
B
open paren f circ g close paren times x is equal to 2 x
C
open paren f circ g close paren times x is equal to x plus 2
D
open paren f circ g close paren times x is equal to x over 2
7

If f of x is equal to x squared minus 2 and g of x is equal to x minus 3 , what is open paren f circ g close paren times x ?

A
open paren f circ g close paren times x is equal to x squared plus 7
B
open paren f circ g close paren times x is equal to x squared minus 3 x plus 7
C
open paren f circ g close paren times x is equal to x squared minus 6 x plus 7
D
open paren f circ g close paren times x is equal to x squared minus 5
8

If f of x is equal to 1 over x and g of x is equal to x plus 3 , which of the following is the graph of open paren f circ g close paren times x ?

A
Image with description On a coordinate plane, the scale on the x axis range from negative 9 to 1 in increments of 1, and the scale on the y axis range from negative 5 to 5 in increments of 1. The curve originates from (negative 7 point 5 comma 0) and crosses the y axis at nonsignificant numbers. The curve lies in the 3rd and 4th quadrants.
B
Image with description On a coordinate plane, the x and y axes list from negative 5 to 5 in increments of 1. The graph is made up of two different curves that do not meet. One of the curves opens up and to the right in quadrant 1 and passes through the point (1 comma 1). The other curve opens down and to the left in quadrant 3 and passes through the point (negative 1 comma negative 1).
C
Image with description On a coordinate plane, the scale on the x axis range from negative 8 to 2 in increments of 1, and the scale on the y axis range from negative 5 to 5 in increments of 1. The graph is made up of two different curves that do not meet. One of the curves opens up and to the right in quadrants 1 and 2 and passes through the point (negative 2 comma 1). The curve crosses the x axis at nonsignificant numbers. The other curve opens down and to the left in quadrant 3 and passes through the point (negative 4 comma negative 1).
D
Image with description On a coordinate plane, the scale on the x axis range from negative 5 to 5 in increments of 1, and the scale on the y axis range from negative 2 to 8 in increments of 1. The graph is made up of two different curves that do not meet. One of the curves opens up to the right in quadrant 1 and passes through the point (1 comma 4). The other curve opens down and to the left in quadrants 2 and 3 and passes through the point (negative 1 comma 2). The curve crosses the x axis at nonsignificant numbers.
9

If f of x is equal to 1 over x and g of x is equal to x minus 2 , which of the following is the graph of open paren f circ g close paren times x ?

A
Image with description On a coordinate plane, the scale on the x axis range from negative 7 to 2 in increments of 1, and the scale on the y axis range from negative 5 to 5 in increments of 1. The graph is made up of two different curves that do not meet. One of the curves opens up and to the right in quadrants 1 and 2 and passes through the point (negative 1 comma 1). The curve crosses the x axis at nonsignificant numbers. The other curve opens down and to the left in quadrant 3 and passes through the point (negative 3 comma negative 1).
B
Image with description On a coordinate plane, the x and y axes list from negative 5 to 5 in increments of 1. The graph is made up of two different curves that do not meet. One of the curves opens up and to the right in quadrant 1 and passes through the point (1 comma 1). The other curve opens down and to the left in quadrant 3 and passes through the point (negative 1 comma negative 1).
C
Image with description On a coordinate plane, the scale on the x axis range from negative 3 to 7 in increments of 1, and the scale on the y axis range from negative 5 to 5 in increments of 1. The graph is made up of two different curves that do not meet. One of the curves opens up to the right in quadrant 1 and passes through the point (3 comma 1). The other curve opens down and to the left in quadrants 3 and 4 and passes through the point (1 comma negative 1). The curve crosses the y axis at nonsignificant numbers.
D
Image with description On a coordinate plane, the scale on the x axis range from negative 5 to 5 in increments of 1, and the scale on the y axis range from negative 7 to 3 in increments of 1. The graph is made up of two different curves that do not meet. One of the curves opens up to the right in quadrants 1 and 5 and passes through the point (1 comma negative 3). The curve crosses the x axis at nonsignificant numbers. The other curve opens down and to the left in quadrant 3 and passes through the point (negative 1 comma negative 3).
10

If f of x is equal to 2 x and g of x is equal to square root of x , what is the domain of open paren f circ g close paren times x ?

A
x is greater than or equal to 0
B
x is not equal to 0
C
x is less than or equal to 0
D
all real numbers

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