write the domain and range of the function using interval notation. then analyze the intercepts and…

write the domain and range of the function using interval notation. then analyze the intercepts and asymptotes. f(x)=e^(x - 8)-1 determine the y - intercept of f(x)=e^(x - 8)-1. select the correct choice below and, if necessary, fill in the answer box to complete a. the y - intercept is (0,1/e^8 - 1) (type an ordered pair. type an exact answer in terms of e.) b. there is no y - intercept. the asymptote of f(x)=e^(x - 8)-1 is (type an equation.)

write the domain and range of the function using interval notation. then analyze the intercepts and asymptotes. f(x)=e^(x - 8)-1 determine the y - intercept of f(x)=e^(x - 8)-1. select the correct choice below and, if necessary, fill in the answer box to complete a. the y - intercept is (0,1/e^8 - 1) (type an ordered pair. type an exact answer in terms of e.) b. there is no y - intercept. the asymptote of f(x)=e^(x - 8)-1 is (type an equation.)

Answer

Explanation:

Step1: Recall y - intercept definition

Set (x = 0) in (y=f(x)=e^{x - 8}-1).

Step2: Calculate y - value

When (x = 0), (y=e^{0 - 8}-1=e^{-8}-1=\frac{1}{e^{8}}-1). So the y - intercept is the point ((0,\frac{1}{e^{8}}-1)).

Step3: Find the asymptote

For the exponential function (y = e^{x - 8}-1), as (x\to-\infty), (e^{x - 8}\to0). So (y = e^{x - 8}-1\to - 1). The horizontal asymptote is (y=-1).

Answer:

The y - intercept is ((0,\frac{1}{e^{8}}-1)) The asymptote of (f(x)=e^{x - 8}-1) is (y = - 1)