Functions

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input. It can be represented as a set of ordered pairs, a table, or a graph.

Front

What is a proportional function?

Back

A proportional function is a type of linear function that passes through the origin (0,0) and can be expressed in the form y = kx, where k is a constant.

Front

How can you determine if a table represents a function?

Back

A table represents a function if each input (x-value) corresponds to exactly one output (y-value). If any input has multiple outputs, it is not a function.

Front

What is the vertical line test?

Back

The vertical line test is a method used to determine if a graph represents a function. If any vertical line intersects the graph at more than one point, the graph is not a function.

Front

What does it mean for a relation to be a function?

Back

For a relation to be a function, each input must be associated with exactly one output. This means no x-value can map to more than one y-value.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the significance of the slope in a linear function?

Back

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

Front

How do you identify a non-function from a set of ordered pairs?

Back

A non-function can be identified if any x-value in the set of ordered pairs is repeated with different y-values.

Front

What is a linear equation that models a decreasing function?

Back

A linear equation that models a decreasing function has a negative slope. For example, y = -3x + 5 represents a decreasing function.

Front

What is the relationship between the x-intercept and y-intercept in a linear function?

Back

The x-intercept is the point where the graph crosses the x-axis (y=0), and the y-intercept is where it crosses the y-axis (x=0). Both are key points in graphing a linear function.