Linear vs. Nonlinear Functions Day 3

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not graph to a straight line. Its rate of change is not constant, and it can take various forms such as quadratic, exponential, or logarithmic.

Front

What does it mean for a relation to be a function?

Back

A relation is a function if every input (x-value) has exactly one output (y-value).

Front

How can you identify a linear function from a graph?

Back

A linear function will graph as a straight line, and it will have a constant slope.

Front

How can you identify a nonlinear function from a graph?

Back

A nonlinear function will graph as a curve or a line that changes direction, indicating a variable rate of change.

Front

What is the slope of a linear function?

Back

The slope of a linear function is the ratio of the change in y to the change in x (rise over run), indicating the steepness of the line.

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, represented by the value of y when x = 0.

Front

What is an example of a linear function?

Back

An example of a linear function is f(x) = 2x + 3, which graphs as a straight line.

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is f(x) = x^2, which graphs as a parabola.

Front

What does a table of values for a linear function look like?

Back

A table of values for a linear function will show a constant difference in the y-values for equal increments in the x-values.