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Chapter 9: Q9. (page 597)

Describe how the graph of each function is related to the graph of f(x)=x2.

g(x)=鈭�3x2

Short Answer

Expert verified

The graph g(x)=鈭�3x2 is the graph of role="math" localid="1647861417429" f(x)=鈥夆赌�x2reflected across the x鈥� axis and vertically stretched by a factor 3.

Step by step solution

01

Step 1. State the concept.

Vertical Stretch and Vertical Compression:

y=af(x),a>1. Sketch the graph f(x)vertically by a factor of a.

y=af(x),0<a<1. Compress the graph f(x)vertically by a factor of a.

02

Step 2. Graph each function.

The graph of the functionsf(x)=x2 andg(x)=鈭�3x2 is given by:

03

Step 3. State the interpretation of the graph.

The graph of f(x)=ax2stretches or compress the parent graph vertically. The coefficient of x2term is negative, so the graph is reflected across the x鈥� axis. Since a=3, the graph is vertically stretched.

Therefore, the graph of g(x)=鈭�3x2is the graph of f(x)=x2reflected across the x鈥� axis and vertically stretched by a factor 3.

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