QuestionCompare the graphs of $f(x)=x^{2}$ and $g(x)=4x^{2}$ . Which statement is true about their relationship?

Studdy Solution

STEP 1

Assumptions1. The function $f(x) = x^{}$ is a standard quadratic function. . The function $g(x) =4x^{}$ is a modified version of $f(x)$ .
3. The modification to $f(x)$ to create $g(x)$ is a multiplication by4.
4. The multiplication by4 does not change the x-values, only the y-values.

STEP 2

We need to understand how the multiplication by4 affects the graph of $f(x)$ . Let's compare the y-values of $f(x)$ and $g(x)$ for the same x-values.

STEP 3

Choose a value for x, say x =1, and plug it into both $f(x)$ and $g(x)$ .
$f(1) =1^{2} =1$ $g(1) = \times1^{2} =$

STEP 4

We can see that the y-value of $g(x)$ is four times the y-value of $f(x)$ for the same x-value. This means that the graph of $g(x)$ is a vertical stretch of the graph of $f(x)$ by a factor of4.

STEP 5

Therefore, the correct statement is C. The graph of $g(x)$ is the graph of $f(x)$ vertically stretched by a factor of4.

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