Analyzing Tables to Define Linear Functions

This lesson covers the definition and identification of linear functions through tables and graphs. It explains the concept of a constant rate of change, represented by the slope 'm', and how changing 'm' affects the slope but not the linearity of the function. Examples include a back-to-school offer, a function with a negative slope, and museum visit costs, illustrating linear functions with different slopes. The lesson also contrasts linear functions with a nonlinear example involving the area of a square, highlighting the absence of a constant rate of change.

What is the defining characteristic of a linear function when represented on a graph?

• It has a variable rate of change.

• It passes through the y-axis.

• It has a constant rate of change.

• It forms a curved line.

In the example of binders and notebooks, what does the function b = n represent?

• The number of notebooks is double the number of binders.

• The number of binders is equal to the number of notebooks.

• The number of notebooks is unrelated to the number of binders.

• The number of binders is half the number of notebooks.

Why do linear functions not always have a 1:1 input-output ratio?

• Because the function is nonlinear.

• Because the input is always greater than the output.

• Because the slope can vary.

• Because the graph is not a straight line.

What is the rate of change for the function y = -3/2x?

• -3/2

• 3/2

• -2/3

• 2/3

How can you verify the constant rate of change in a linear function?

• By checking if the graph is a curve.

• By calculating the change in output over the change in input.

• By ensuring the function passes through the origin.

• By comparing the input values only.

What does a constant rate of change indicate about a function?

• The function is linear.

• The function has no slope.

• The function is quadratic.

• The function is nonlinear.

In the function A = s^2, why is it considered nonlinear?

• Because the rate of change varies.

• Because the input and output are equal.

• Because the rate of change is constant.

• Because it forms a straight line on a graph.