Functions and Rate of Change

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 initial value in a graph?

Back

The initial value is the y-coordinate of the point where the graph intersects the y-axis.

Front

How do you find the rate of change in a linear function?

Back

The rate of change is found by calculating the change in the y-values divided by the change in the x-values (rise over run).

Front

What does a non-proportional relationship look like on a graph?

Back

A non-proportional relationship does not pass through the origin and has a y-intercept that is not zero.

Front

What is the equation for a linear function?

Back

The equation for a linear function is typically in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean for a relationship to be proportional?

Back

A proportional relationship means that the ratio of the two quantities is constant and the graph passes through the origin.

Front

How can you tell if a relation is a function from a graph?

Back

A relation is a function if any vertical line drawn through the graph intersects it at most once.

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 is the cost equation for a pizzeria that charges $12 per pizza and $3 for delivery?

Back

The cost equation is c = 12p + 3, where c is the total cost and p is the number of pizzas.

Front

What does it mean if a function is not linear?

Back

If a function is not linear, it means that its graph does not form a straight line and may curve or change direction.