Comparing Functions

Question

What key features do the functions f(x) = 4^-x and  have in common?

 a. Both f(x) and g(x) include domain values of [–4, ∞) and range values of (–∞, ∞), and both functions have an x-intercept in common. 

b. Both f(x) and g(x) include domain values of [4, ∞), and both functions decrease over the interval (4, ∞). 

c. Both f(x) and g(x) include domain values of [4, ∞) and range values of [0, ∞), and both functions have a y-intercept in common. 

d. Both f(x) and g(x) include domain values of [–4, ∞) and range values of (–∞, ∞), and both functions are negative for the entire domain.

Answer 1

Hey!

So, to begin, we want to look at the graphs of these functions to make them easier to compare.

The first is an exponential function, based on e^-x. The y-intercept will always be (0,1) for either the positive exponential or the negative exponential functions. Here, the constant 4 doesn't change that, and barely makes a difference in the input/output values "close" to the origin.

The second is a square root function. The major thing is knowing how to find the domain of ANY square root function (setting the radical >/= to 0 and then solving for x). The next objective would be to find the range.

I hope this helps!