How do you find vertical, horizontal and oblique asymptotes for $h (x) = 5^{x - 2}$ $h(x)=5^(x-2)$ ?

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How do you find vertical, horizontal and oblique asymptotes for $h (x) = 5^{x - 2}$ $h(x)=5^(x-2)$ ?

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Answer 1 · 2018-01-25T09:27:52

$y = 0$ $y=0$

Explanation:

The function $f (x) = 5^{x}$ $f(x)=5^x$ has horizontal asymptote $y = 0$ $y=0$ because as $x \to - \infty$ $x to -oo$ , $f (x) \to 0$ $f(x) to 0$ and no other asymptotes.

$h (x) = 5^{x} - 2$ $h(x)=5^x-2$ is a horizontal shift of $f (x)$ $f(x)$ by 2 units to the right, so the range is not impacted. That means the horizontal asymptote is still $y = 0$ $y=0$ . The function has no other asymptotes.

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How do you find vertical, horizontal and oblique asymptotes for $h (x) = 5^{x - 2}$ $h(x)=5^(x-2)$ ?

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Explanation:

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How do you find vertical, horizontal and oblique asymptotes for h(x)=5^(x-2)h(x)=5x−2h(x)=5^(x-2)?

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How do you find vertical, horizontal and oblique asymptotes for $h (x) = 5^{x - 2}$ $h(x)=5^(x-2)$ ?