Unit #3 Envision functions and relations

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

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

How can you determine if a relation is a function?

Back

A relation is a function if no x-value is repeated. This can be checked using the vertical line test on a graph.

Front

What does it mean for a function to have a constant rate of change?

Back

A function has a constant rate of change if the difference in y-values divided by the difference in x-values is the same for any two points on the line.

Front

What is the slope of a linear function?

Back

The slope of a linear function is a measure of how steep the line is, calculated as the rise (change in y) over the run (change in x).

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

What is the difference between a function and a non-function?

Back

A function has one output for each input, while a non-function may have multiple outputs for a single input.

Front

What is an example of a linear function?

Back

An example of a linear function is f(x) = 2x + 3, which creates a straight line when graphed.

Front

What is the vertical line test?

Back

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

Front

What does it mean for a function to be nonlinear?

Back

A nonlinear function does not create a straight line when graphed. It may curve or have varying slopes.