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 y-value.

Front

What is function notation?

Back

Function notation is a way to represent functions using symbols. The most common notation is f(x), where 'f' is the name of the function and 'x' is the input variable.

Front

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

Back

No, it is not a function because the input '1' is associated with two different outputs (2 and 4).

Front

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

Back

Yes, it is a function because each input has exactly one output.

Front

What does f(x) = 2x + 3 represent?

Back

This represents a linear function where the output is determined by multiplying the input x by 2 and then adding 3.

Front

How do you find f(-2) if f(x) = x^2 + 1?

Back

f(-2) = (-2)^2 + 1 = 4 + 1 = 5.

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

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

Back

f(3) = 3^2 = 9.

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, it is not a function.