Chapter 9, Problem 6PT

To determine

To graph and describe the relation between the given function to the graph of the function $f(x)=x^2$ .

Explanation of Solution

Given information :

Given functions is $g(x)=x^2-5$ .

Graph :

  

Interpretation :

The graph represented by $g(x)=x^2+k$ is equivalent to the graph of $f(x)=x^2$ that has been translated vertically. The direction of translation or movement of the graph is dependent on the value of k .

If $k>0$ , the graph of $f(x)=x^2$ is translated $\left|k\right|$ units upwards.

If $k<0$ , the graph of $f(x)=x^2$ is translated $\left|k\right|$ units downwards.

In the function $g(x)=x^2-5$ , the value of $k<0$ at $k=-5$ . Therefore, the relation of the function with respect to the graph of $f(x)=x^2$ , as seen in the graph shown above, can be described as a downward translation by $5$ units.