# How do you find the domain and range for y = -.566021616 (x - 6) ^2 + 3.7?

Sep 2, 2015

See below.

#### Explanation:

$y = - 0.566021616 {\left(x - 6\right)}^{6} + 3.7$

$x$ can take any value, so the domain is all real numbers.

When $x = 6$, ${\left(x - 6\right)}^{6} = 0$, and $y = 3.7$.

When x ≠ 6, ${\left(x - 6\right)}^{6}$ is a positive number, and $- 0.566021616 {\left(x - 6\right)}^{6}$ is a negative number.

So $3.7$ is the maximum value of $y = - 0.566021616 {\left(x - 6\right)}^{6} + 3.7$.

The range is all real numbers less than or equal to $3.7$.