Question

question 1-6
function f is defined by f(x) = 5^x.
part a
select the domain of the function
part b
select the range of the function
part c
select the asymptote of the function
part d
select the y - intercept of the function

Explanation:

Step1: Find domain of $f(x)=5^x$

The domain of an exponential function with a positive base is all real numbers, since we can raise 5 to any real power.

Step2: Find range of $f(x)=5^x$

For any real $x$, $5^x$ is always positive and can take any positive real value, so the range is all positive real numbers.

Step3: Find asymptote of $f(x)=5^x$

As $x\to-\infty$, $5^x\to0$, so the horizontal asymptote is the line $y=0$.

Step4: Find y-intercept of $f(x)=5^x$

Substitute $x=0$ into the function: $f(0)=5^0=1$.

Answer:

Part A: All real numbers ($(-\infty, \infty)$)
Part B: All positive real numbers ($(0, \infty)$)
Part C: $y=0$ (horizontal asymptote)
Part D: $(0, 1)$