Chapter 7.3, Problem 6QR

Solution

a.

To identify: The $\left(0,-1\right)$ points are on the graph of the function.

  $\begin{array}{c}f\left(x\right)=x^3-4x-1\\ \text{a}.\left(0,-1\right)\end{array}$

Yes $\left(0,-1\right)$ is on the graph of the function.

Given information:

  $\begin{array}{c}f\left(x\right)=x^3-4x-1\\ \text{a}.\left(0,-1\right)\end{array}$

Explanation:

Consider the given information.

To determine out if a point is on a function, you must plug in the point to see if the function work.

  $\begin{array}{c}f\left(x\right)=x^3-4x-1\\ -1={\left(0\right)}^3-4\left(0\right)-1\\ -1=-1\end{array}$

So, $\left(0,-1\right)$ is on the graph of the function.

b.

To identify: The $\left(-2,-17\right)$ points are on the graph of the function.

  $\begin{array}{c}f\left(x\right)=x^3-4x-1\\ \text{b}\text{.}\left(-2,-17\right)\end{array}$

No $\left(-2,-17\right)$ is on the graph of the function.

Given information:

  $\begin{array}{c}f\left(x\right)=x^3-4x-1\\ \text{b}\text{.}\left(-2,-17\right)\end{array}$

Explanation:

Consider the given information.

Once again, plug the point into the function. Because the answer does not equal the $y$ ,the point is not a part of the function

  $\begin{array}{c}f\left(x\right)=x^3-4x-1\\ -17={\left(-2\right)}^3-4\left(-2\right)-1\\ -17\ne -1\end{array}$

So, $\left(-2,-17\right)$ is not on the graph of the function.