Question

I really need help I've answered mainly all the questions but i need some assistance with these few!!! Please show all work, so I can look how you found your answers THANK YOU SM!!!!

Use the function f(x)= - 4^x-1 - 2 to answer the questions below.
1.) State the equation for the asymptote.
2.)What is the range?
3.)What is the domain?
4.) Finally which axis is f(x) reflected over and what caused the reflection?

Answer 1

See below for answers and explanations

Explanation:

I assume the function you wrote was
`f(x)=-4^(x-1)-2`

1) The equation for the horizontal asymptote is y=-2 since a function of the form f(x) = a(b^x) + c always has a horizontal asymptote at y = c, so c=-2, therefore the horizontal asymptote equation is y=-2

2) The range is (-∞,-2) since any real value of y that is less than -2 but doesn't equal -2 (since it's not included) will be a solution.

3) The domain is (-∞,∞) since any real value of x will be a solution.

4) The axis that f(x) is reflected over is the x-axis because when you negate a base in an exponential function, that will occur.