Questions: Use transformations of f(x)=1/x^2 to graph g(x)=1/(x+6)^2. Which of the following transformations of f(x) need to be applied to graph g(x)? Choose the correct answer below A. The graph of f(x)=1/x^2 should be shifted to the left 6 units to obtain the graph of g(x)=1/(x+6)^2. B. The graph of f(x)=1/x^2 should be shifted down 6 units to obtain the graph of g(x)=1/(x+6)^2 C. The graph of f(x)=1/x^2 should be shifted to the right 6 units to obtain the graph of g(x)=1/(x+6)^2 D. The graph of f(x)=1/x^2 should be shifted up 6 units to obtain the graph of g(x)=1/(x+6)^2.

Use transformations of f(x)=1/x^2 to graph g(x)=1/(x+6)^2.

Which of the following transformations of f(x) need to be applied to graph g(x)? Choose the correct answer below
A. The graph of f(x)=1/x^2 should be shifted to the left 6 units to obtain the graph of g(x)=1/(x+6)^2.
B. The graph of f(x)=1/x^2 should be shifted down 6 units to obtain the graph of g(x)=1/(x+6)^2
C. The graph of f(x)=1/x^2 should be shifted to the right 6 units to obtain the graph of g(x)=1/(x+6)^2
D. The graph of f(x)=1/x^2 should be shifted up 6 units to obtain the graph of g(x)=1/(x+6)^2.
Transcript text: MyLab, Math All Test 3 (Sections MyLab Math All Warning Pears son.com/Student/PlayerTest aspx?testld=264508718 (MATH-1111-O7F-08F) s 2.6, 2.7, 3.1, 3.2, 3.5) Question 12 of 20 Use transformations of $f(x)=\frac{1}{x^{2}}$ to graph $g(x)=\frac{1}{(x+6)^{2}}$. Which of the following transformations of $\mathrm{f}(\mathrm{x})$ need to be applied to graph $\mathrm{g}(\mathrm{x})$ ? Choose the correct answer belon A. The graph of $f(x)=\frac{1}{x^{2}}$ should be shifted to the left 6 units to obtain the graph of $g(x)=\frac{1}{(x+6)^{2}}$. B. The graph of $f(x)=\frac{1}{x^{2}}$ should be shifted down 6 units to obtain the graph of $g(x)=\frac{1}{(x+6)^{2}}$ C. The graph of $f(x)=\frac{1}{x^{2}}$ should be shifted to the right 6 units to obtain the graph of $g(x)=\frac{1}{(x+6)^{2}}$ D. The graph of $f(x)=\frac{1}{x^{2}}$ should be shifted up 6 units to obtain the graph of $g(x)=\frac{1}{(x+6)^{2}}$. Select the correct graph
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Solution

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Solution Steps

Step 1: Identify the transformation

The function \( g(x) = \frac{1}{(x+6)^2} \) is a transformation of \( f(x) = \frac{1}{x^2} \). The transformation involves a horizontal shift. Specifically, the function \( g(x) \) is obtained by shifting \( f(x) \) to the left by 6 units.

Final Answer

A. The graph of \( f(x) = \frac{1}{x^2} \) should be shifted to the left 6 units to obtain the graph of \( g(x) = \frac{1}{(x+6)^2} \).

{"axisType": 3, "coordSystem": {"xmin": -10, "xmax": 10, "ymin": -1, "ymax": 10}, "commands": ["y = 1/x2", "y = 1/(x+6)2"], "latex_expressions": ["$y = \\frac{1}{x^2}$", "$y = \\frac{1}{(x+6)^2}$"]}

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