Identifying Linear and Non-Linear Functions

Mrs. Yaod teaches math students about comparing linear and non-linear functions. The lesson covers identifying linear functions through graphs, x-y tables, and equations. Students learn to recognize linearity by checking for constant changes in x and y values and rewriting equations in the form y=mx+b. The video includes examples and graphing exercises to reinforce the concepts.

What is the primary characteristic of a linear function?

• It forms a U-shape on a graph.

• It forms a straight line on a graph.

• It always decreases as x increases.

• It has a variable exponent greater than one.

How can you visually identify a non-linear function on a graph?

• It is always horizontal.

• It changes direction or curves.

• It has a constant slope.

• It forms a straight line.

In an x-y table, what indicates a linear function?

• Both x and y change by constant amounts.

• The x values are all the same.

• Both x and y change by different amounts.

• The y values are all the same.

What is a key feature of a non-linear function in an x-y table?

• The y values decrease by the same amount.

• The x values decrease by the same amount.

• The y values increase by different amounts.

• The x values increase by the same amount.

Which form must an equation be in to confirm it is linear?

• y = mx + b

• y = ax^3 + bx^2 + cx + d

• y = ax^2 + bx + c

• y = a/x

Why is the equation y = 4/x considered non-linear?

• It can be rewritten as y = mx + b.

• It has x in the denominator.

• It has a constant slope.

• It forms a straight line.

What does the presence of an exponent greater than one in an equation indicate?

• The function is constant.

• The function is undefined.

• The function is linear.

• The function is non-linear.

When graphing data from a table, what suggests the function is non-linear?

• The x values are negative.

• The points form a curve.

• The points form a straight line.

• The y values are all positive.

In graphing, what does it mean if the plotted points form a straight line?

• The function is undefined.

• The function is non-linear.

• The function is linear.

• The function is quadratic.

What is the significance of constant changes in x and y values in a table?

• It indicates a non-linear function.

• It indicates an exponential function.

• It indicates a linear function.

• It indicates a quadratic function.