Interpreting Graphs and Variables

Interpret graphical representations and variable meanings. Math 10-C Alberta mathematics.

Lesson 7.3 of Relations and Functions in Math 10C: Alberta curriculum lessons.

What you'll learn in this lesson

• Independent and Dependent Variables. Learn which variable is the input and which is the output, and how to identify each role in a real-world situation.
• Reading a Graph: The Scuba Dive. Practise reading a real-world line graph by pulling domain, range, and key facts from a diver's depth-over-time graph.
• Reading More Graphs: Watering Can and People. Analyse two more graphs: a continuous watering-can scenario and a discrete scatter plot, and decide whether each is a function.
• Connecting the Dots, When to Join Points. Decide when to connect data points based on whether the data is discrete or continuous, and read domain and range from line-segment graphs.

Inside the lesson: a free preview

The Two Roles

The Critical Rule. The independent variable is the input, it goes on the x-axis.

The dependent variable is the output, it goes on the y-axis and depends on the independent variable.

How to Tell Them Apart

The Cause Test. Ask: "Which one causes the other to change?"

The cause is the independent variable.

The result is the dependent variable.

Worked Example: Bus Tickets. A bus sells tickets at \2.00 each. Money collected depends on how many tickets are sold.

Step 1: Identify the cause:

The number of tickets sold drives the total. You choose (or observe) how many tickets sell. That is the input.

Step 2: Identify the result:

The total price responds to the ticket count. It cannot be known until you know how many tickets sold.

Step 3: Assign roles:

Independent variable: the number of tickets sold.

Dependent variable: the total price collected.

Watch the Wording. A question might list both variables together: "the price or the amount of tickets sold."

Do not let the order of the words in the sentence mislead you. Always apply the cause test:

The number of tickets is the input, and the total price is the output.

Is It a Function?. Each number of tickets sold gives exactly one total price (tickets × \2.00).

One input → one output.

Yes, this is a function.

Worked example: Worked Example: Birds vs. Temperature

A researcher records the number of bird species heard and the temperature at different times over 24 hours.

Joe's Graph: Number of Species vs. Time. You cannot hear "half a species." The values between whole numbers have no meaning.

This data is discrete → the points should not be connected.

Alice's Graph: Temperature vs. Time. Temperature flows continuously: it passes through every value between readings. A reading of 18.6°C is perfectly meaningful.

This data is continuous → the points can be connected.

Are They Relations and Functions?. Are they relations? Yes. Both pair time with a measurement.

Are they functions? Yes. Each clock time gives one reading in each graph. Both pass the vertical line test.

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