Functions

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 graph of a function. If any vertical line intersects the graph more than once, it is not a function.

Front

What does it mean for a function to be linear?

Back

A linear function is a function that graphs to a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is the difference between independent and dependent variables?

Back

The independent variable is the input of a function (often x), while the dependent variable is the output (often y) that depends on the input.

Front

What is a constant function?

Back

A constant function is a function that does not change its value; it has the form f(x) = c, where c is a constant.

Front

What is the slope of a line?

Back

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

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as the input values increase, the output values also increase.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing if, as the input values increase, the output values decrease.

Front

What is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions for different intervals of the input.

Front

What is a domain in a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.