Question

graphing rational functions: mastery test
the graph of \\(h(x) = g(x + 5)\\) has choose an answer and choose an answer
options for first dropdown:

• choose an answer
• the same horizontal asymptote as function g
• a horizontal asymptote at y = 5
• a horizontal asymptote at y = 8

Explanation:

Identify asymptotes of the graphed function \(g(x)\)

Using the Rational Function Asymptotes knowledge point

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Analyze the transformation from \(g(x)\) to \(h(x)\)

Using the Horizontal and Vertical Translations knowledge point

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$$

Determine the asymptotes of the transformed function \(h(x)\)

Using the Rational Functions knowledge point

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$$

Match with the dropdown options

Comparing the calculated asymptotes to the visible dropdown options:

• The horizontal asymptote remains \(y = 3\), which corresponds to "the same horizontal asymptote as function g".
• The vertical asymptote shifts to \(x = -7\), which corresponds to "a vertical asymptote at x = -7".

Answer:

The graph of \(h(x) = g(x + 5)\) has <blank>the same horizontal asymptote as function g</blank> and <blank>a vertical asymptote at \(x = -7\)</blank>.