Question

(0, -2) Correct or not?

What is the y-intercept of the exponential function?

f(x)= -1/8 (4) ^x+3 +6

y-intercept =

Answer 1

make f(x) = y
f(x)= -1/8 (4) ^x+3 +6
y = -1/8 (4) ^x+3 +6
y-intercept is when the function crosses the y-axis, and the y-axis is always where x = 0
y = -1/8 (4) ^x+3 +6

`y = -1/8 ( {4}^(0))+9 \\ {(anything)}^(0) = 1 \\ y = -1/8 (1)+9 = 9 - (1 / 8) \\ = 8 \: (7 / 8)`
or was the equation instead:

`y = -1/8 ( {4}^((x + 3)))+6`
???????
Because in that case it's totally different, so here goes...

`y = -1/8 ( {4}^((x + 3)))+6 \\ y = -1/8 ( {4}^((0 + 3)))+6 \\ y = -1/8 ( {4}^(3))+6 \\ y = -1/8 (64)+6`

`y = -1/1 (8)+6 = - 8 + 6 = - 2`
Therefore, yes it is correct that the y-intercept lies at the point (0, -2)