Q. 19 - Precalculus Enhanced with Graphing Utilities

Question

Graph the function $f$ by starting with the graph of $y=x^2$ and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility.

$f\left(x\right)=\frac{1}{4}{x}^2$

Step-by-Step Solution

Answer

The required graph is shown below:

Step 1. Given information.

The given function is:

$f\left(x\right)=\frac{1}{4}{x}^2$

Step 2. Determine the transformations used.

In the function $f\left(x\right)=a(x-h{)}^2+k$, $a$ is a constant and $(h,k)$ is the vertex.

In the given function $a=\frac{1}{4},h=0,k=0$. So, the graph of $y=x^2$ is vertically compressed by factor 4.

First, plot the graph of $y=x^2$ then divide the values by 4 to get the graph of $f\left(x\right)=\frac{1}{4}{x}^2$.

Step 3. Draw the graph.

The required graph is shown below:

Using a graphing utility, we get a graph that is the same as the above graph.