NEW CHARACTERISTICS OF FUNCTIONS

Front

What is a function?

Back

A function is a relation where every input (x-value) has exactly one output (y-value).

Front

What are x-intercepts?

Back

X-intercepts are points where the graph of a function crosses the x-axis, meaning the output (y-value) is zero.

Front

What is f(0) in a function?

Back

f(0) is the output of the function when the input is 0.

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, as x increases, f(x) also increases.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing on an interval if, as x increases, f(x) decreases.

Front

What is an interval of increase?

Back

An interval of increase is a range of x-values where the function's output is rising.

Front

What is an interval of decrease?

Back

An interval of decrease is a range of x-values where the function's output is falling.

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.

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 over the change in x (rise/run).

Front

What is the y-intercept?

Back

The y-intercept is the point where the graph of a function crosses the y-axis (x=0).