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Can somebody help me find the Domain, Range, Horizontal Asymptote, Y-Intercept, and End Behavior of the function f(x) = -2e^x + 4 ?

User DrGary
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4 votes

Answer:

Domain = R

Range = (-∞, 4)

Hor. asymp = y=4

Y intercept: f(0) = (0,2)

end behaviour:

x → -∞: f(x) → 4

x→ ∞: f(x) → -∞

Explanation:

For the domain, it is R because e^x works for all values of x

For the range, y will never be above 4.

The hor. asymptote is found via
\lim_(x \to -\infty) f(x) there the e term will be zero, so what is left is y=4.

Y intercept, fill in f(0)

end behaviour: for small x, y goes to the asymptote, for large x, y goes to minus infinity.

User Oleg Fridman
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