Functions & Slope

Front

What is the definition of 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 the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise (change in y) over the run (change in x).

Front

How do you determine if a set of ordered pairs represents a function?

Back

A set of ordered pairs represents a function if no two different pairs have the same first element.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as x increases, y also increases, meaning the line rises from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, meaning the line falls from left to right.

Front

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

Back

The formula is m = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the slope-intercept form.

Front

What does it mean if a function is not a function?

Back

If a relation is not a function, it means that at least one input is associated with more than one output.

Front

How can you visually identify a function on a graph?

Back

You can use the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.