Understanding Functions 5.1-5.3 Quick Check

Front

What is a function?

Back

A function is a relation where each input has exactly one output.

Front

What is not a function?

Back

A relation where an input has more than one output is not a function.

Front

How can you determine if a relation is a function?

Back

Use the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of the function; it indicates how steep the line is.

Front

What is the formula for calculating slope?

Back

Slope (m) = (change in y) / (change in x) = (y2 - y1) / (x2 - x1).

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.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the y-intercept?

Back

The y-intercept is the point where the line crosses the y-axis (x=0).

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as x increases, y also increases.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing if, as x increases, y decreases.