Functions Study Guide

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 the 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.

Front

Is the set of values (9,5) (10,5) (9,-5) (10,-5) a function?

Back

No, it is not a function because the input 9 is associated with two different outputs (5 and -5).

Front

Is the set of values (6,-5) (7,-3) (8,-1) (9,1) a function?

Back

Yes, it is a function because each input is associated with 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 over run between two points on the line.

Front

How do you find the slope from the equation 8x - 24y = 32?

Back

Rearranging to slope-intercept form (y = mx + b) gives m = 1/3.

Front

What does a slope of 0 indicate?

Back

A slope of 0 indicates a horizontal line, meaning there is no change in y as x changes.

Front

What does a positive slope indicate?

Back

A positive slope indicates that as x increases, y also increases.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as x increases, y decreases.

Front

What is the definition of a linear function?

Back

A linear function is a function that graphs to a straight line, represented by the equation y = mx + b.