# What is the range of the function y=8x-3?

Nov 29, 2017

Range of $y$ is $\left(- \infty , + \infty\right)$

#### Explanation:

$y = 8 x - 3$

First note that $y$ is a straight line with slope of $8$ and $y -$intercept of $- 3$

The range of a function is the set of all valid outputs ("$y -$ values") over its domain.

The domain of all straight lines (other than the vertical ones) is $\left(- \infty , + \infty\right)$ since they are defined for all values of $x$

Hence, the domain of $y$ is $\left(- \infty , + \infty\right)$

Also, since $y$ has no upper or lower bounds, the range of $y$ is also $\left(- \infty , + \infty\right)$

Nov 29, 2017

$- \infty \le y \le \infty$ (all real numbers ($R$))

#### Explanation:

Just remember that the range for a linear function is always all real numbers unless it is horizontal (doesn't have $x$).

One example of a linear function with a range of not all real numbers would be $f \left(x\right) = 3$. The range for this function would be $y = 3$.

I hope that helps!