Identifying and Evaluating 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

How can you determine if a relation is a function?

Back

A relation is a function if every input (x-value) has exactly one output (y-value). This can be checked using the vertical line test on a graph.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a function. If a vertical line intersects the curve at more than one point, then the curve is not a function.

Front

Evaluate f(x) = 4x + 5 at x = 4.

Back

f(4) = 4(4) + 5 = 16 + 5 = 21.

Tags

CCSS.HSF.IF.A.2

Front

Evaluate g(x) = 5 - 6x at x = -5.

Back

g(-5) = 5 - 6(-5) = 5 + 30 = 35.

Tags

CCSS.HSF.IF.A.2

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What does it mean for a function to be linear?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.HSF.LE.A.2

CCSS.8.F.B.4

Front

What is a slope in a linear function?

Back

The slope of a linear function is a measure of how steep the line is, calculated as the change in y divided by the change in x (rise/run).

Tags

CCSS.8.EE.B.5

Front

What is a y-intercept?

Back

The y-intercept is the point where the graph of a function crosses the y-axis, represented as (0, b) in the function f(x) = mx + b.