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Chapter 3: Q. 55 (page 139)

Under what circumstances is a linear function f(x)=mx+b odd? Can a linear function ever be even?

Short Answer

Expert verified

A linear function f(x)=mx+bwill be odd if and only if b=0

A linear function f(x)=mx+bwill be an even function if the slopem=0and it is a constant function.

Step by step solution

01

Step 1. Given information

The given linear function is

f(x)=mx+b

02

Step 2. Odd function

If the y-intercept of a linear function f(x)=mx+bthen the line will pass through the origin

f(x)=mx+bf(x)=mxf(-x)=m-xf(-x)=-mxf(-x)=-f(x)

So a linear function will be an odd function if itsy-interceptb=0

03

Step 3. Even function

A liner will be a constant function if its slope m=0

f(x)=mx+bf(x)=bf(-x)=bf(-x)=f(x)

So a linear function will even function if its slopelocalid="1647291567428" m=0

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