Functions and Function Notation

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.

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 variable.

Front

What does it mean for a set of values to be a function?

Back

A set of values is a function if no two different ordered pairs have the same first element.

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.

Front

What is the horizontal line test?

Back

The horizontal line test determines if a function is one-to-one. If any horizontal line intersects the graph of the function more than once, it is not one-to-one.

Front

How do you evaluate a function?

Back

To evaluate a function, substitute the input value into the function's equation and simplify to find the output.

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 f(x) = x^2 - x + 3 represent?

Back

This represents a quadratic function where the output is calculated by squaring the input, subtracting the input, and adding 3.

Front

If f(x) = 2x + 1, what is f(3)?

Back

f(3) = 2(3) + 1 = 7.