Question

(0, -2) Correct or not?

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
$y = -1/8 ( {4}^{0})+9 \\ {(anything)}^{0} = 1 \\ y = -1/8 (1)+9 = 9 - (1 \div 8) \\ = 8 \: (7 \div 8)$
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)