1Cademy - Example: Reading Function Values, Intercepts, Domain, and Range from a Graph (Variant 1)

Learn Before

Graph of a Mathematical Function

Example

Example: Reading Function Values, Intercepts, Domain, and Range from a Graph (Variant 1)

By analyzing the visual graph of a mathematical function, its properties can be determined directly from the plotted points. Consider a periodic wavy graph that extends infinitely left and right along the $x$ -axis. Because it spans all real $x$ -values, its domain is $(-\infty, \infty)$ . The graph strictly oscillates vertically, reaching its highest points at a $y$ -value of $2$ and its lowest points at a $y$ -value of $-2$ , making its range $[-2, 2]$ . To evaluate the function at specific inputs, locate the corresponding point on the curve. For example, to find $f\left(\frac{1}{2}\pi\right)$ , identify the point $\left(\frac{1}{2}\pi, 2\right)$ on the graph, which indicates that $f\left(\frac{1}{2}\pi\right) = 2$ . Similarly, the point $\left(-\frac{3}{2}\pi, 2\right)$ shows that $f\left(-\frac{3}{2}\pi\right) = 2$ . The $x$ -intercepts occur where the graph crosses the $x$ -axis, such as at $(-2\pi, 0)$ , $(-\pi, 0)$ , $(0, 0)$ , $(\pi, 0)$ , and $(2\pi, 0)$ ; these correspond to the solutions for $f(x) = 0$ . The graph crosses the $y$ -axis precisely at the origin, meaning the $y$ -intercept is $(0, 0)$ , which also corresponds to the evaluation $f(0) = 0$ .

0

1

Updated 2026-05-26

Contributors are:

Who are from:

References

OpenStax Intermediate Algebra

Learn Before

Related

Learn After