Question

find the horizontal asymptote for the following exponential function. remember to type in your answer as a function.

$f(x)=7^{3x + 6}-7$

your answer is

question help: video read written example

Explanation:

Step1: Analyze the general form of exponential function

The general form of an exponential function is \(y = a\cdot b^{kx + c}+d\). For \(y = 7^{3x + 6}-7\), here \(a = 1\), \(b = 7\), \(k = 3\), \(c = 6\), \(d=-7\).

Step2: Determine the horizontal asymptote

For an exponential function \(y = a\cdot b^{kx + c}+d\), when \(|b|>1\) (in our case \(b = 7>1\)), as \(x\to-\infty\), \(b^{kx + c}\to0\). So \(y\to d\).

Answer:

\(y=-7\)