AVERAGE RATE OF CHANGE/ LINEAR FUNCTION

Front

What is the average rate of change?

Back

The average rate of change of a function over an interval is the change in the function's value divided by the change in the input value over that interval.

Front

How do you calculate the average rate of change from 20 to 40 minutes?

Back

Average Rate of Change = (f(40) - f(20)) / (40 - 20). For example, if f(40) = 0 and f(20) = -40, then the average rate of change is (0 - (-40)) / (40 - 20) = 2 gallons per minute.

Front

What is the slope of a line?

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 an undefined slope indicate?

Back

An undefined slope indicates a vertical line, where the x-coordinates are the same for two points, resulting in division by zero.

Front

What is a function?

Back

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

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, where m is the slope and b is the y-intercept.

Front

What does a zero slope indicate about a line?

Back

A zero slope indicates a horizontal line, meaning there is no change in y as x changes.

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 exactly one output for each input.

Front

How can you determine if a graph represents 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 is the formula for slope between two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1).