Comparing Functions - Flashcard

Front

What is a linear relationship?

Back

A linear relationship is a relationship between two variables that can be represented by a straight line on a graph. It has a constant rate of change.

Front

What is the equation of a linear function?

Back

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

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the dependent variable (y) with respect to the independent variable (x).

Front

What is the vertical line test?

Back

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

Front

What is a function?

Back

A function is a relation that assigns exactly one output (y) for each input (x).

Front

What is the difference between a function and a relation?

Back

A relation can have multiple outputs for a single input, while a function must have only one output for each input.

Front

What is a rate of change?

Back

The rate of change is a measure of how much a quantity changes in relation to another quantity, often expressed as a ratio.

Front

How do you find the rate of change from a table of values?

Back

To find the rate of change from a table, calculate the difference in the y-values divided by the difference in the x-values for two points.

Front

What does it mean for two functions to have the same rate of change?

Back

Two functions have the same rate of change if their slopes are equal, indicating they increase or decrease at the same rate.

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers used to represent a point in a coordinate system, written in the form (x, y).