Question

How do you find the y intercepts for `q(x) = -7^(x-4) -1`?

Answer 1

The y -intercept is at `-(1+1/1401)`
(but see note below).

Explanation:

The y-intercept is where the function crosses the y-axis; for all points on the y-axis, `x=0`.

When `x=0`
`color(white)("XXXX")` `g(x)` (also know as `y`) `= -7^(x-4)-1`
`color(white)("XXXX")`becomes
`color(white)("XXXX")` `g(0) = -7^-4-1`
`color(white)("XXXX")` `color(white)("XXXX")` `= - 1/(7^4) -1` see note below
`color(white)("XXXX")` `color(white)("XXXX")` `= -(1+1/1401)`

note
This assumes `-7^(x-4)` is interpreted as `-(7^(x^4))` and not as `(-7_^(x-4))`. If this is not the case the correct answer would be `-(1-1/1401)`