AnswersMathematics IIIAnalyzing Compositions of Functions

Analyzing Compositions of Functions — Quiz Answers

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If f of x is equal to the fraction with numerator x minus 3 and denominator x , g of x is equal to x plus 3 , and h of x is equal to 2 x plus 1 , what is open paren g circ h circ f close paren times x ?

A
open paren g circ h circ f close paren times x is equal to the fraction with numerator 8 x plus 1 and denominator 2 x plus 1
B
open paren g circ h circ f close paren times x is equal to the fraction with numerator 3 x minus 6 and denominator x
C
open paren g circ h circ f close paren times x is equal to the fraction with numerator 2 x plus 4 and denominator 2 x plus 7
D
open paren g circ h circ f close paren times x is equal to the fraction with numerator 6 x minus 6 and denominator x
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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 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).
B
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.
C
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.
D
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).
23

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

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