Evaluate Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented in the Cartesian plane 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 does the slope of a linear function represent?

Back

The slope of a linear function 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

How do you find the y-intercept of a linear function?

Back

The y-intercept of a linear function is found by setting x = 0 in the function's equation and solving for y.

Front

Evaluate f(-4) for the function f(x) = 2x + 3.

Back

f(-4) = 2(-4) + 3 = -8 + 3 = -5.

Front

Evaluate f(5) for the function f(x) = 2x + 3.

Back

f(5) = 2(5) + 3 = 10 + 3 = 13.

Front

What is the function notation for a linear function?

Back

The function notation for a linear function is typically written as f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is the y-intercept of the equation y = -3x + 7?

Back

The y-intercept is 7.

Front

Find f(0) for the function f(x) = -3x + 3.

Back

f(0) = -3(0) + 3 = 3.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By + C = 0, where A, B, and C are constants.

Front

How do you determine if a function is linear?

Back

A function is linear if it can be expressed in the form f(x) = mx + b, where m and b are constants.