How to Find the X and Y Intercepts of a Function

Finding the x and y intercepts of a function is an essential skill in algebra, as it helps you understand the function’s behavior. Let’s break it down step by step.

1. Finding the Y-Intercept:

The y-intercept of a function is the point where the graph crosses the y-axis. To find the y-intercept, follow these steps:

1. Set the value of x to zero in the function.
2. Solve the resulting equation for y.
3. The y-intercept is then the point (0, y).

Example:

Consider the function f(x) = 2x + 3. To find the y-intercept:

1. Set x = 0: f(0) = 2(0) + 3 = 3.
2. The y-intercept is (0, 3).

2. Finding the X-Intercept:

The x-intercept is the point where the graph crosses the x-axis. To find the x-intercept, follow these steps:

1. Set the value of y to zero in the function.
2. Solve the resulting equation for x.
3. The x-intercept is then the point (x, 0).

Example:

Using the same function f(x) = 2x + 3, let’s find the x-intercept:

1. Set y = 0: 0 = 2x + 3.
2. Solve for x: 2x = -3 → x = -3/2.
3. The x-intercept is (-3/2, 0).

In summary, to find the y-intercept, set x to zero and solve for y, and for the x-intercept, set y to zero and solve for x. By identifying these intercepts, you can better understand the function’s graph and its overall behavior.