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

find the horizontal asymptote for the following exponential function. remember to type in your answer as a function.\n\n$f(x)=7^{3x + 6}-7$\n\nyour answer is\n\nquestion help: video read written example

find the horizontal asymptote for the following exponential function. remember to type in your answer as a function.\n\n$f(x)=7^{3x + 6}-7$\n\nyour answer is\n\nquestion help: video read written example

Answer

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)