Identifying Functions

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. In other words, for every x-value, there is one and only one y-value.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It 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. Examples include quadratic functions, exponential functions, and trigonometric functions.

Front

Identify the function: y = 2x + 3

Back

This is a linear function.

Front

Identify the function: y = x^2 - 4

Back

This is a nonlinear function.

Front

What is the slope of the line represented by the function y = 4x + 1?

Back

The slope is 4.

Front

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

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x = 0.

Front

How can you determine if a relation is a function from a set of ordered pairs?

Back

A relation is a function if no two ordered pairs have the same first element (x-value).

Front

What is the difference between a function and a relation?

Back

A relation is any set of ordered pairs, while a function is a specific type of relation where each input is associated with exactly one output.

Front

What is a vertical line test?

Back

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