What are the synonymous terms for the points where a function's graph crosses the x-axis?

Conditions

• The function is being viewed as a graph in the coordinate plane.
• The context is solving $f(x) = 0$.

Reasoning, step by step

1. Identify the x-values where the function output is 0.
2. Recognize that these points represent the intersection of the graph with the x-axis.
3. Use the terms zero, x-intercept, root, or solution interchangeably to describe these x-values.

Example

The speaker lists terms: 'zero', 'intercept', 'root', 'solution', emphasizing that these are the points the theorem helps us locate intervals for.

Common misconceptions

• Thinking that 'root' and 'solution' only apply to equations, not to graphs.
• Confusing x-intercepts with y-intercepts.

Watch the explanation

Explore next

• How do I find intervals where a function has a zero using a table of values?
• Why does a change from positive to negative imply a zero for a continuous function?