Comparing 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.

Tags

CCSS.8.F.A.1

Front

What does the slope of a line represent in a function?

Back

The slope represents the rate of change of the function; it indicates how much the output (y) changes for a unit change in the input (x).

Tags

CCSS.8.EE.B.5

Front

How do you determine the rate of change from a graph?

Back

The rate of change can be determined by calculating the slope of the line on the graph, which is the rise over run (change in y over change in x).

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

What is the difference between a positive slope and a negative slope?

Back

A positive slope indicates that as x increases, y also increases, while a negative slope indicates that as x increases, y decreases.

Tags

CCSS.8.EE.B.5

Front

What does it mean for two functions to have the same slope?

Back

It means that both functions change at the same rate; for every unit increase in x, the increase in y is the same for both functions.

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

Front

How can you compare the steepness of two lines?

Back

You can compare the steepness by looking at their slopes; the line with the greater absolute value of the slope is steeper.

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

Front

What is the formula for calculating the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Tags

CCSS.8.EE.B.5

Front

What does it mean if two functions intersect at a point?

Back

If two functions intersect at a point, it means they have the same output (y-value) for the same input (x-value) at that point.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is the y-intercept of a function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, which occurs when x = 0.