# What is the domain and range of #g(x) = x^2 + 7x -18 #?

##### 1 Answer

Sep 20, 2015

Domain is all

Range is

#### Explanation:

This is a 2nd degree quadratic polynomial so its graph is a parabola.

Its general form is

The domain is all possible x values that are allowed as inputs and so in this case is all real numbers

The range is all possible output y values that are allowed and so since the turning point occurs when the derivative equals zero,

The corresponding y value is then

Hence the range

I have included the graph underneath for extra clarity.

graph{x^2+7x-18 [-65.77, 65.9, -32.85, 32.9]}