Power Functions - Graphs

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What is a power function?

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What does the graph of a power function look like when n is positive?

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The graph of a power function with a positive exponent (n > 0) is a curve that increases as x increases.

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What does the graph of a power function look like when n is negative?

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The graph of a power function with a negative exponent (n < 0) approaches the x-axis as x increases and has a vertical asymptote at x = 0.

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What is the significance of the constant k in a power function?

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The constant k affects the vertical stretch or compression of the graph. If k > 1, the graph stretches; if 0 < k < 1, it compresses.

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How does the value of n affect the shape of the graph of a power function?

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The value of n determines the degree of the function and the number of turns in the graph. Even n results in a U-shaped graph, while odd n results in an S-shaped graph.

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What is a vertical asymptote?

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A vertical asymptote is a vertical line x = a where the function approaches infinity or negative infinity as x approaches a.