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Q. 46

Expert-verifiedFound in: Page 114

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.

$f\left(x\right)={\left(x+2\right)}^{3}-3$

The graph of the function is given as:

The domain and the range of the given function are all real numbers.

The parent function of the given function is __$g\left(x\right)={x}^{3}$.__

So, the graph of $g\left(x\right)={x}^{3}$ is given as:__ __

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

Similarly, for $h\left(x\right)={\left(x+2\right)}^{2}$, the graph localid="1645807375470" $g\left(x\right)={x}^{3}$ is shifted to the left by localid="1645807379159" $2$ unis.

The graph is given as:

We know that for,$y=f\left(x\right)-k$, the original graph is shifted downwards by $k$ units.

Similarly, for $f\left(x\right)={\left(x+2\right)}^{3}-3$, the graph is shifted downwards by $3$ units.

The graph of the given function is:

From the graph, we infer that

The domain and the range of the given function are all real numbers.

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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