Question

The domain and range of the graph above

Answer 1

Answers:

• Domain: $\boldsymbol{(-\infty, \infty)}$
• Range: $\boldsymbol{[3,\infty)}$

Note that there's a square bracket for the '3', but everything else is a curved parenthesis.

==================================================

Explanation:

The domain is the set of all allowed x inputs. The arrows tell us that the parabola stretches forever in both left and right directions. We can plug in any x value we want, which means the domain is the set of all real numbers which means the interval notation for that is $(-\infty, \infty)$

This is the same as writing the compound inequality $-\infty < x < \infty$

--------------

The range is the set of all possible y values. The lowest output is y = 3, which is where the vertex is located. We can have this output or anything larger.

So y = 3 or larger, which we can write $y \ge 3$ and that flips to $3 \le y$ and further expands into $3 \le y < \infty$

The interval notation for the range is therefore $[3 ,\infty)$. We use a square bracket to include 3 as part of the range.