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Q. 40

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Found in: Page 113

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

# Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. Verify your results using a graphing utility. $f\left(x\right)={x}^{2}+4$

The graph of the function $f\left(x\right)={x}^{2}+4$ is given as:

The domain of the function is $\left(-\infty ,\infty \right)$ and the range is $\left[4,\infty \right)$

See the step by step solution

## Step 1. given data

The given function is $f\left(x\right)={x}^{2}+4$

## Step 2. Graph the parent function.

The parent function of the given function is $g\left(x\right)={x}^{2}$

Plot the graph of the function$g\left(x\right)={x}^{2}$

## Step 3. Graph of the function

Graph of function$f\left(x\right)={x}^{2}+4$ can be obtained by shifting the graph of the function $g\left(x\right)={x}^{2}$ upward by $4$units

The graph of the function is given as:

## Step 4.  domain and range of the function

From the graph, we infer that

The domain of the function is $\left(-\infty ,\infty \right)$

The range of the function is $\left[4,\infty \right)$

## Step 5. Verification

plot the graph of the function $f\left(x\right)={x}^{2}+4$using a graphing utility

The graph is the same as we have drawn. Hence, it is correct.