Finding the X-Intercept and Zero of a Function from a Graph

Graphical Analysis of Linear Functions

X-Intercept and Zero of a Function

In College Algebra, understanding how to interpret the graph of a function is essential. The x-intercept and the zero of a function are closely related concepts that can be identified visually from the graph.

• X-Intercept: The x-intercept of a function is the point where the graph crosses the x-axis. At this point, the value of y is zero.

• Zero of a Function: The zero of a function is the value of x for which $f(x) = 0$. This is the same as the x-coordinate of the x-intercept.

From the given graph:

• The blue line crosses the x-axis at x = -5.

• Therefore, the x-intercept is (-5, 0).

• The zero of the function is x = -5.

Definitions

• X-Intercept: The point $(x, 0)$ where the graph of a function crosses the x-axis.

• Zero of a Function: The value $x$ such that $f(x) = 0$.

Example

• Suppose the function is $f(x) = x + 5$. Setting $f(x) = 0$ gives:

$x + 5 = 0$ $x = -5$

• Thus, the zero of the function is $x = -5$, and the x-intercept is $(-5, 0)$.

Key Points

• The x-intercept and the zero of the function are the same for any function $f(x)$: the x-value where $f(x) = 0$.

• To find the x-intercept from a graph, look for the point where the graph crosses the x-axis.