Functions and Function Notation

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. In other words, for every x-value, there is one and only one corresponding y-value.

Front

What is function notation?

Back

Function notation is a way to represent functions using symbols. For example, f(x) represents a function named 'f' evaluated at the input 'x'.

Front

Is the mapping {(1, 2), (2, 3), (3, 4)} a function?

Back

Yes, this mapping is a function because each input (1, 2, 3) has a unique output (2, 3, 4).

Front

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

Back

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

Front

What does it mean for a relation to not be a function?

Back

A relation is not a function if at least one input is associated with more than one output.

Front

Given f(x) = x^2, what is f(-3)?

Back

f(-3) = (-3)^2 = 9.

Front

How do you determine if a table of values represents a function?

Back

Check if any x-value is repeated. If an x-value appears more than once with different y-values, it is not a function.

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

If f(x) = 3x - 5, what is f(2)?

Back

f(2) = 3(2) - 5 = 6 - 5 = 1.