Chapter 9, Problem 8SGR

To determine

To state if true or false.

Answer to Problem 8SGR

False. The graph of the parent function is translated upwards translated down to form the graph of $f(x)=x^2+5$

Explanation of Solution

Given information :

The graph of the parent function is translated downwards translated down to form the graph of $f(x)=x^2+5$

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 $f(x)=x^2+5$ , 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 an upward translation by $5$ units.