Interpret key features of graphs (intercepts, maxima/minima, intervals of increase/decrease). | Functions | ACT Mathematics

Read intercepts, turning points, and intervals to understand how a graph behaves.

Core Idea

Key graph features tell you how a function behaves without solving every point. Intercepts show where the graph crosses the axes, and turning points tell you where the function switches from increasing to decreasing or the reverse.

Understanding

Rule: When ACT asks about a graph, look first for the big landmarks: $𝑥$ -intercepts, $𝑦$ -intercept, vertex or turning point, and the direction the graph opens or ends. Those features often answer the question faster than substituting numbers into the equation.

For intervals of increase and decrease, focus on what happens as you move left to right. If the graph rises, the function is increasing. If it falls, the function is decreasing. A maximum or minimum usually marks the change between those intervals.

Misconceptions

Mixing up the $𝑥$ -coordinate of a vertex with the interval itself.
Reading intercepts as turning points.
Forgetting that intervals of increase and decrease are written in terms of $𝑥$ -values, not points on the graph.

Question

Worked Example

A parabola opens downward, has $𝑥$ -intercepts at $- 1$ and $5$ , and has vertex $(2, 9)$ . On which interval is the function increasing?

Select an answer to see the explanation