Identifying Linear Functions & Function Notation

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 function notation?

Back

Function notation is a way to represent functions in mathematics. It uses symbols like f(x) to denote the output of a function f for a given input x.

Front

How do you determine if a function is linear or nonlinear?

Back

A function is linear if it can be expressed in the form f(x) = mx + b. If it cannot be expressed in this form, it is nonlinear.

Front

What does the slope (m) represent in a linear function?

Back

The slope (m) represents the rate of change of the function. It indicates how much the output (y) changes for a unit change in the input (x).

Front

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

Back

The y-intercept (b) is the value of the function when the input (x) is 0. It is the point where the line crosses the y-axis.

Front

If f(x) = 3/2 x - 4, what is f(0)?

Back

f(0) = 3/2(0) - 4 = -4.

Front

If f(x) = 3/2 x - 4, what is the output when x = 4?

Back

f(4) = 3/2(4) - 4 = 6 - 4 = 2.

Front

What is the input (x) if f(x) = 2 for the function f(x) = 3/2 x - 4?

Back

To find x, set 2 = 3/2 x - 4. Solving gives x = 4.

Front

What is the input (x) if f(x) = -1 for the function f(x) = 3/2 x - 4?

Back

To find x, set -1 = 3/2 x - 4. Solving gives x = 2.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not form a straight line when graphed. It can have curves, bends, or other shapes.