Functions & Function Notation

Front

What is a function?

Back

A function is a relation that assigns exactly one output value for each input value.

Tags

CCSS.8.F.A.1

Front

What is function notation?

Back

Function notation is a way to represent functions using symbols, typically written as f(x), where f is the function name and x is the input.

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1

Front

How can you determine if a graph represents a function?

Back

A graph represents a function if no vertical line intersects the graph at more than one point (Vertical Line Test).

Front

What does it mean for a function to be linear?

Back

A linear function is a function that graphs to a straight line and can be expressed in the form f(x) = 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 slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept of a function?

Back

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

Front

Evaluate the function f(x) = 2x + 3 for f(4).

Back

f(4) = 2(4) + 3 = 8 + 3 = 11.

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 one-to-one?

Back

A function is one-to-one if it never assigns the same value to two different domain elements, meaning each output is unique.