In this lesson, students work with graphs and tables that represent functions in addition to the equations and descriptions used previously. They learn the conventions of graphing the independent variable (input) on the horizontal axis and the dependent variable (output) on the vertical axis and that each coordinate point represents an input-output pair of the function.
By matching contexts and graphs and reading information about functions from graphs and tables, students become familiar with the different representations and draw connections between them.
- Determine whether a graph represents a function, and explain (orally) the reasoning.
- Identify the graph of an equation that represents a function, and explain (orally and in writing) the reasoning.
- Interpret (orally and in writing) points on a graph, including a graph of a function and a graph that does not represent a function.
Let’s connect equations and graphs of functions.
- I can identify graphs that do, and do not, represent functions.
- I can use a graph of a function to find the output for a given input and to find the input(s) for a given output.
A dependent variable represents the output of a function.
For example, suppose we need to buy 20 pieces of fruit and decide to buy apples and bananas. If we select the number of apples first, the equation \(b=20-a\) shows the number of bananas we can buy. The number of bananas is the dependent variable because it depends on the number of apples.
An independent variable represents the input of a function.
For example, suppose we need to buy 20 pieces of fruit and decide to buy some apples and bananas. If we select the number of apples first, the equation \(b=20-a\) shows the number of bananas we can buy. The number of apples is the independent variable because we can choose any number for it.
A radius is a line segment that goes from the center to the edge of a circle. A radius can go in any direction. Every radius of the circle is the same length. We also use the word radius to mean the length of this segment.
For example, \(r\) is the radius of this circle with center \(O\).