Q. 1 - 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.

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

Step-by-Step Solution

Answer

(a) The slope is $2$ and $y$-intercept is $-2.$

(b) The average rate of change of $f\left(x\right)$ is $2.$

(c) The graph of $f\left(x\right)$ is

(d) The function is increasing.

Part (a) Step 1. Given information

It is given that $f\left(x\right)=2x-5.$ We need to determine the slope and $y$-intercept of each linear function.

Step 2. Simplify

The given function is, $f\left(x\right)=2x-5.$ If the function is $f\left(x\right)=mx+b$ then $m$ is the slope and $b$ is the $y$-intercept of the function. So, the slope is $m=2$ and $y$-intercept is $b=-5$ for the linear function $f\left(x\right)=2x-5.$

Part (b) Step 1. Given information

It is given that $f\left(x\right)=2x-5.$ We need to determine the average of the change of the function.

Step 2. Conclusion

We know that the average rate of change is the same as the slope is $2.$

Part (c) Step 1. Given information

It is given that $f\left(x\right)=2x-5.$ We need to graph the function and label the intercept.

Step 2. Graphing

The graph of $f\left(x\right)$ is

Part (d) Step 1. Given information

The given function is $f\left(x\right)=2x-5.$ We need to determine whether the function is increasing, decreasing, or constant.

Step 2. Conclusion

As we increase the value of the argument $x$ the function values rise so the function is increasing all the time.