How do you find the domain and range of root4(-4-7x)?

Jan 17, 2018

The domain is $x \in \left(- \infty , - \frac{4}{7}\right]$. The range is $y \in \left[0 , + \infty\right)$

Explanation:

Let $y = {\left(- 4 - 7 x\right)}^{\frac{1}{4}}$

What's under the square root sign is $\ge 0$

Therefore,

$- 4 - 7 x \ge 0$

$7 x \le - 4$

$x \le - \frac{4}{7}$

The domain is $x \in \left(- \infty , - \frac{4}{7}\right]$

When $x = - \frac{4}{7}$, $\implies$, $y = 0$

When $x = - \infty$, $\implies$, $y = + \infty$

The range is $y \in \left[0 , + \infty\right)$

graph{(-4-7x)^(1/4) [-12.66, 12.65, -6.33, 6.33]}