Q. 2 - Precalculus Enhanced with Graphing Utilities

Question

In Problems 1–3:

(a) Determine the slope and y-intercept of each linear function.

(b) Find the average rate of change of each function.

(c) Graph each function. Label the intercepts.

(d) Determine whether the function is increasing, decreasing, or constant.

$F\left(x\right)=-\frac{1}{3}x+1$

Step-by-Step Solution

Answer

Slope$=-\frac{1}{3}$

y-intercept$=(0,1)$

Rate of change$=-\frac{1}{3}$

The given function is decreasing.

Part (a) Step 1. Given Information

$F\left(x\right)=-\frac{1}{3}x+1$

Part (a) Step 2. Calculation

Since $F\left(x\right)=-\frac{1}{3}x+1$

Clearly, the slope of the above function is, $m=-\frac{1}{3}$

Part (b) Step 1. Given Information

$F\left(x\right)=-\frac{1}{3}x+1$

Part (b) Step 2.

Since $F\left(x\right)=-\frac{1}{3}x+1$

Then the rate of change is equal to the slope of the function$=-\frac{1}{3}$

Pat (c) Step 1. Given Information

$F\left(x\right)=-\frac{1}{3}x+1$

Part (c) Step 2. Graph

Part (d) Step 1. Given Information

$F\left(x\right)=-\frac{1}{3}x+1$

Part (d) Step 2. Calculation

Since the slope of the given function is negative i.e. $-\frac{1}{3}$.

 Then the function is decreasing.