Question

find the asymptote and y-intercept of the following function.
y = -3·4^x
show your work here
asymptote: y =
y-intercept y =

Explanation:

Step1: Find horizontal asymptote

For exponential functions of the form $y = a \cdot b^x$, as $x \to -\infty$, $b^x \to 0$. So:
$$\lim_{x \to -\infty} (-3 \cdot 4^x) = -3 \cdot 0 = 0$$

Step2: Calculate y-intercept

Set $x=0$ (since y-intercept occurs at $x=0$):
$$y = -3 \cdot 4^0 = -3 \cdot 1 = -3$$

Answer:

Asymptote: $y = 0$
y-intercept: $y = -3$