Understanding Intercepts in Functions

When you're studying Year 11 math, knowing about intercepts is super important. Intercepts tell us about how a function’s graph looks, and there are two types: x-intercepts and y-intercepts.

1. What are Intercepts?

• X-Intercepts:

  • These are the points where the graph meets the x-axis.
  • This means that at these points, the function's value is zero.
  • To find the x-intercepts, we set the function equal to zero, or $f(x) = 0$.
  • For example, if we have the function $f(x) = x^2 - 4$, the x-intercepts are $x = 2$ and $x = -2$.

• Y-Intercepts:

  • This is the point where the graph crosses the y-axis.
  • To find it, we calculate $f(0)$.
  • For the same function, $f(0) = -4$, so the y-intercept is at the point (0, -4).

2. Why Are Intercepts Important?

• Graphing:

  • Knowing the intercepts can make it easier to draw the graph.
  • With just these points, you can create a simple shape of the function.

• Analyzing Behavior:

  • Intercepts help us understand how the function behaves.
  • For example, if there are no x-intercepts, that means the function never crosses the x-axis.
  • This can tell us if the function is always positive or negative.

By focusing on intercepts, you can make studying functions and their behaviors easier to understand!