Chapter 3, Problem 1RE

In Problems 1-3:

(a) Determine the slope and $y\text{-intercept}$ 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.

1. $f\left(x\right) =2x - 5$

To determine

To calculate:

a. The slope and $y\text{-intercept}$ of the given function.

b. Average rate of change of the given function.

c. Graph the given function and label the intercepts.

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

Answer to Problem 1RE

Solution:

a. The slope of the given function is 2 and $-5$ is the $y\text{-intercept}$.

b. 2

c. Increasing.

Explanation of Solution

Given:

The given equation is

$f(x)=2x-5$

Formula used:

For a linear function of the form $f(x)=mx+b$, $m$ is the slope and $b$ is the $y\text{-intercept}$.

The average rate of change of the linear function is the slope of that function.

The function is said to be increasing in it domain, then its slope is positive.

The function is said to be decreasing in it domain, then its slope is negative.

The function is said to be constant if the slope is 0.

Calculation:

a. From the definition of the linear function, the slope of the given function is 2 and $-5$ is the $y\text{-intercept}$.

b. The average rate of change of the given function is 2.

c. Using the given function, we can see that

$x$	$f(x)=2x-5$
$-2$	$-9$
$-1$	$-7$
$0$	$-5$
$1$	$-3$
$2$	$-1$
$3$	$1$

Thus, the graph of the given function is

(d) Since the slope of the given function is positive, the function is increasing.