Understanding Functions

Front

Is it a function?

Back

A relation is a function if each input has exactly one output. If an input has multiple outputs, it is NOT a function.

Front

What is the rate of change of a linear function?

Back

The rate of change of a linear function is the slope, which represents how much the output (y) changes for a unit change in the input (x).

Front

What makes a graph proportional?

Back

A graph is proportional if it is linear and passes through the origin (0,0).

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a slope?

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

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if each output is produced by exactly one input, meaning no two different inputs map to the same output.

Front

What is a dependent variable?

Back

A dependent variable is the output of a function, typically represented as y, which depends on the value of the independent variable (x).

Front

What is an independent variable?

Back

An independent variable is the input of a function, typically represented as x, which can be freely chosen without depending on other variables.

Front

What is a 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.