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Chapter 2: Q. 1 (page 164)

Slope and linear functions: If f is a linear function with slope -3such that f(2)=1,find the following, without first finding an equation for f(x).

f(4)f(7)f(-2)

Short Answer

Expert verified

Function values are following.

f(4)=-8f(7)=-17f(-2)=10

Step by step solution

01

Step 1. Given information.

The given slope of the linear function is m=-3.

The given function value isf(2)=1.

02

Step 2. Value of f(4).

Substitute y=f(4),x=4,m=-3,x0=2,&y0=1in standard point-slope form of a linear equation and solve for y.

y-y0=m(x-x0)f(4)-1=-3(4-1)f(4)-1=-9f(4)=-8

So function value isf(4)=-8

03

Step 3. Value of f(7).

Substitute y=f(7),x=7,m=-3,x0=2,&y0=1in standard point-slope form of a linear equation and solve for y.

y-y0=m(x-x0)f(7)-1=-3(7-1)f(7)-1=-18f(7)=-17

So function value isf(7)=-17.

04

Step 4. Value of f(-2).

Substitute y=f(-2),x=-2,m=-3,x0=2,&y0=1in standard point-slope form of a linear equation and solve for y.

role="math" localid="1649800928489" y-y0=m(x-x0)f(-2)-1=-3(-2-1)f(-2)-1=9f(-2)=10

So function value isf(-2)=10.

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