QuestionFind the graph of $g(x)=\frac{1}{4} f(x)$ given $f(x)=x^{2}$ .

Studdy Solution

STEP 1

Assumptions1. The function $f(x)=x^{}$ is given. . We need to find the graph of the function $g(x)=\frac{1}{4} f(x)$ .

STEP 2

First, we need to express the function $g(x)$ in terms of $x$ by substituting $f(x)$ with $x^{2}$ .
$g(x)=\frac{1}{4} f(x)$

STEP 3

Substitute $f(x)$ with $x^{2}$ .
$g(x)=\frac{1}{} x^{2}$

STEP 4

Now that we have the function $g(x)$ expressed in terms of $x$ , we can plot it. The graph of $g(x)$ is a parabola that opens upwards, similar to the graph of $f(x)$ , but it is vertically compressed by a factor of $\frac{1}{4}$ .
This means that the graph of $g(x)$ will be wider than the graph of $f(x)$ , because every y-value in the graph of $f(x)$ is divided by4 to get the corresponding y-value in the graph of $g(x)$ .
To plot the graph, we can choose some values for $x$ and calculate the corresponding values for $g(x)$ .

STEP 5

Choose some values for $x$ and calculate the corresponding values for $g(x)$ .
For example, if $x=-2, -1,0,1,2$ , then $g(-2)=\frac{1}{4} (-2)^{2} =1$ $g(-1)=\frac{1}{4} (-1)^{2} =0.25$ $g(0)=\frac{1}{4} (0)^{2} =0$ $g(1)=\frac{1}{4} (1)^{2} =0.25$ $g(2)=\frac{1}{4} (2)^{2} =1$

STEP 6

Plot these points on the graph and draw a smooth curve through them to get the graph of $g(x)$ .
The graph of $g(x)=\frac{1}{4} x^{2}$ is a parabola that opens upwards and is wider than the graph of $f(x)=x^{2}$ .

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