Chapter 3 Flashcard

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, and it can include quadratic, exponential, and other types of functions.

Front

How can you determine if a set of points represents a linear function?

Back

If the differences in the y-values divided by the differences in the x-values (the slope) are constant for all pairs of points, the function is linear.

Front

Given the points (3, 9), (6, 36), (9, 81), (12, 144), (15, 225), is the function linear or nonlinear?

Back

Nonlinear.

Front

Given the points (-5, 5), (-4, 4), (-3, 3), (-2, 2), (-1, 1), is the function linear or nonlinear?

Back

Linear.

Front

What does the slope of a linear function represent?

Back

The slope represents the rate of change of the dependent variable with respect to the independent variable.

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the value of the dependent variable when the independent variable is zero (x=0).

Front

Solve for x: f(x) = -2x + 14 when f(x) = 10.

Back

x = 2.

Front

What is the dependent variable in the function c = 75m + 225?

Back

c, which represents the cost of gym membership.

Front

What is the general form of a linear equation?

Back

The general form is Ax + By = C, where A, B, and C are constants.