Chapter 3, Problem 1CT

For the linear function $f\left(x\right)=-4x+3$,

a. Find the slope and $y\text{-intercept}$.

b. Determine whether $f$ is increasing, decreasing, or constant.

c. Graph $f$.

To determine

To calculate:

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

b. Determine whether the given function is increasing, decreasing or constant.

c. Graph the function.

Answer to Problem 1CT

Solution:

a. The slope is $-4$ and the $y\text{-intercept}$ is 3.

b. The function is a decreasing function.

c. The graph is given below.

Explanation of Solution

Given:

The given function is $f(x)=-4x+3$

Formula used:

The equation of a line is $f(x)=mx+c$, where $m$ is the slope and $c$ is the $y\text{-intercept}$.

Calculation:

a. From the given function, we can see that the slope of the function is $m=-4$ and the $y\text{-intercept}$ is 3.

b. Here, we can see that the slope is negative. Therefore, the function is decreasing.

c. The graph of the given function is