Question

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

Answer 1

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.