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Chapter 2: Q. 7 (page 126)

Consider the function

g(x)=2x+1ifx<-1x-4ifx鈮�-1

(a) Graph the function.

(b) List the intercepts.

(c) Find g(-5).

(d) Find g(2).

Short Answer

Expert verified

(a) Graph of function is


(b) the x-intercept is (4,0) and the y-intercept is (0,-4)

(c) value of g(-5)is -9

(d) value of g(2)is -2

Step by step solution

01

Step 1. given data

The given function is

g(x)=2x+1ifx<-1x-4ifx鈮�-1

02

Step 2. Part (a)

Determine the different points for the graph of the function g(x)=2x+1for whichx<-1

Determine the different points for the graph of the function g(x)=x-4for whichx>=-1

03

Step 2. graph of the function

Plot points and connect them through a straight line for the graph of functions

04

Step 4. Part (b)

For thex-intercept,y=0

then x value of g(x)=x-4wheng(x)=0is

g(x)=x-40=x-4x=4

so x-intercept is (4,0)

For they-intercept,x=0soyvalue ofg(x)=x-4 is

g(x)=x-4g(x)=0-4g(x)=-4y=-4

y-intercept is(0,-4)

05

Step 5. Part (c)

x=-5is less than-1, so the function will be g(x)=2x+1

substitute -5 for x in the function

g(x)=2x+1g(-5)=2(-5)+1g(-5)=-10+1g(-5)=-9

06

Step 6. Part (d)

x=2is greater than-1so function will beg(x)=x-4

substitute2forxin the function

g(x)=x-4g(2)=2-4g(2)=-2

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