Identifying Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = 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 form a straight line when graphed. Its rate of change is not constant.

Front

How can you identify a linear function from its graph?

Back

A linear function will graph as a straight line, while a nonlinear function will have curves or bends.

Front

What is the slope of a linear function?

Back

The slope of a linear function is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

Front

What does the y-intercept represent in a linear function?

Back

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

Front

Is the function f(x) = 2x + 3 linear or nonlinear?

Back

Linear Function.

Front

Is the function f(x) = x^2 + 2 linear or nonlinear?

Back

Nonlinear Function.

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input.

Front

How can you determine if a relation is a function?

Back

A relation is a function if each input (x-value) corresponds to exactly one output (y-value).

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function. If a vertical line intersects the graph at more than one point, it is not a function.