Practice connecting functions to their graphs. Graphs help students see input, output, direction, intercepts, and patterns visually.
A point on a graph is written as (x, y). The x-value tells the input, and the y-value tells the output. When reading a graph, move horizontally to find x and vertically to find y.
Problem: A graph contains the point (2, 5). What is the input and output?
Step 1: Read the ordered pair.
The point is (2, 5).
Step 2: Identify the input.
The input is the x-value, so x = 2.
Step 3: Identify the output.
The output is the y-value, so y = 5.
Answer: Input = 2 and output = 5.
You are ready to move on when you can identify x as the input and y as the output from any point on a graph.
Intercepts show where a graph crosses an axis. The x-intercept is where the graph crosses the x-axis. At the x-intercept, y = 0. The y-intercept is where the graph crosses the y-axis. At the y-intercept, x = 0.
Problem: A line crosses the y-axis at (0, 3). What is the y-intercept?
Step 1: The y-intercept happens where x = 0.
Step 2: The point (0, 3) has x = 0.
Step 3: The y-value is 3.
Answer: The y-intercept is 3.
You are ready to move on when you can explain that x-intercepts have y = 0 and y-intercepts have x = 0.
A graph is increasing when it rises from left to right. A graph is decreasing when it falls from left to right. A graph is constant when it stays flat. These patterns help describe how the output changes as the input increases.
Problem: A graph rises from left to right. Is it increasing or decreasing?
Step 1: Look at the graph from left to right.
Step 2: The graph moves upward.
Step 3: When the graph moves upward, the output is increasing.
Answer: The graph is increasing.
You are ready to move on when you can describe graph behavior by reading the graph from left to right.
Different types of equations create different graph shapes. Linear functions usually make straight lines. Quadratic functions make U-shaped curves called parabolas. Constant functions make horizontal lines.
Problem: What graph shape does y = x² make?
Step 1: Look at the variable.
The variable x is squared.
Step 2: Squared functions are quadratic.
Step 3: Quadratic functions make U-shaped graphs.
Answer: y = x² makes a U-shaped graph called a parabola.
You are ready to move on when you can connect common equation types to their graph shapes.
Graphs often represent real situations such as distance, temperature, cost, height, or speed. The x-axis usually shows the input, such as time, and the y-axis usually shows the output, such as distance or amount.
Problem: A distance-time graph rises from left to right. What does that mean?
Step 1: Identify the axes.
The x-axis represents time, and the y-axis represents distance.
Step 2: The graph rises as time increases.
Step 3: The distance is increasing over time.
Answer: The object is moving farther away as time passes.
You are ready to move on when you can connect the graph direction to what is happening in the real situation.