Question

3. **Determine the equation of the asymptote of y = 4(2)^x – 3.

Answer 1

Horizontal asymptote: y = -3

Step-by-step explanation

The horizontal asymptote is the value the function takes when x→∞ or x→-∞. In this case, when x→∞ the function goes to ∞, but when x→-∞:

`\lim _(x\rightarrow-\infty)4(2^{})^x-3=\lim _(x\rightarrow\infty)4(1)/(2^x)-3=\lim _(x\rightarrow\infty)4(1)/(2^x)-\lim _(x\rightarrow\infty)3=0-3=-3`

The equation of the horizontal asyptote is y = -3