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

Jun 15, 2015

The y -intercept is at $- \left(1 + \frac{1}{1401}\right)$
(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 $x = 0$
$\textcolor{w h i t e}{\text{XXXX}}$$g \left(x\right)$ (also know as $y$) $= - {7}^{x - 4} - 1$
$\textcolor{w h i t e}{\text{XXXX}}$becomes
$\textcolor{w h i t e}{\text{XXXX}}$$g \left(0\right) = - {7}^{-} 4 - 1$
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$= - \frac{1}{{7}^{4}} - 1$ see note below
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$= - \left(1 + \frac{1}{1401}\right)$

note
This assumes $- {7}^{x - 4}$ is interpreted as $- \left({7}^{{x}^{4}}\right)$ and not as $\left(- {7}_{^} \left(x - 4\right)\right)$. If this is not the case the correct answer would be $- \left(1 - \frac{1}{1401}\right)$