# What is the domain and range of  f(x) = 2x^2 - 3?

Feb 1, 2018

graph{2x^2-3 [-10.07, 9.93, -3.86, 6.14]} So this shown above $\uparrow$ is the graph for $f \left(x\right) = 2 {x}^{2} - 3$.
Domain: $x = \infty$
Range: $y > - 3$

#### Explanation:

The definition of domain is the set of $x$ values on the graph. The definition of the range is the set of $y$ values on a graph.
So when you look at the domain you look at the $x$-axis (horizontal line). So where does the line stop and start on the $x$-axis? it goes on forever right? Because the side keeps expanding forever and ever so the domain would equal $\infty$ ... Now let's look at the range. The range is the set of y-values so if you have a paper on this tilt it so it's easier to see it looks like a big arrow, <. So the tip of this "arrow" touches -3 and then goes on forever and ever...
so you can either put y>-3 (y is bigger than negative 3) or,
$- 3 < y < \infty$ (-3 is smaller than y but goes on forever).
Hope this was understandable please comment below if you have concerns...