Q. 1 - Precalculus Enhanced with Graphing Utilities

Question

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

(a) Find the slope and y-intercept. 

(b) Determine whether f is increasing, decreasing, or constant. 

(c) Graph f. 

Step-by-Step Solution

Answer

Part (a). Slope is $m=-4$ y-intercept is $b=3$.

Part (b). The function is decreasing.

Part (c). The graph of function is 

Step 1. Given information.

The linear function is given: $f\left(x\right)=-4x+3$.

Part (a) step 1. Find the slope and y-intercept.

The linear function is in the form $f\left(x\right)=mx+b; m\ne 0$.

where m is slope and b is the y-intercept.

After comparing the function $f\left(x\right)=-4x+3$

We get the slope is $m=-4$ and y-intercept is $b=3$.

Part (b) step 1. Determine whether f is increasing, decreasing, or constant.

The given function is $f\left(x\right)=-4x+3$.

As we increases the value of argument of $x$, the function value fall.

So the function is decreasing all the time. 

Part (c) step 1. Graph the functon.

The graph of function is