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Q. 44

Expert-verifiedFound in: Page 113

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.

$h\left(x\right)=\sqrt{x+1}$

The graph of the function is given as:

The domain of the function is $[-1,\infty )$ and the range is $[0,\infty )$

The given function is $h\left(x\right)=\sqrt{x+1}$

The parent function of the given function is $f\left(x\right)=\sqrt{x}$

So, the graph of $f\left(x\right)=\sqrt{x}$ is given as:

We know that for,$y=f(x+k)$, the original graph is shifted to the left by $k$ units.

Similarly, for $h\left(x\right)=\sqrt{x+1}$, the graph $f\left(x\right)=\sqrt{x}$ is shifted to the left by 1 units .

The graph of the given function is given as:

From the graph, we infer that

The domain of the function is $[-1,\infty )$

The range of the function is localid="1645798371444" $[0,\infty )$$[0,\infty )$

The graph of the given function using graphing utility is given as:

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

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