Understand Functions

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and 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 and may include curves, such as quadratic functions like y = x² + 7.

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of the function, indicating how much y changes for a unit change in x.

Front

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

Back

The y-intercept can be found by setting x to 0 in the equation and solving for y.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers.

Front

What is the difference between the slope and the y-intercept?

Back

The slope indicates the steepness of the line, while the y-intercept is the point where the line crosses the y-axis.

Front

What are exponents in relation to functions?

Back

Exponents indicate the power to which a number is raised and can determine if a function is linear or nonlinear.

Front

What is the formula for calculating slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as x increases, y also increases.