Functions Introduction

Front

What is a function?

Back

A function is a relation that assigns exactly one output (y-value) for each input (x-value).

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 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 relation to be a function?

Back

A relation is a function if each input (x-value) is associated with exactly one output (y-value).

Front

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

Back

f(1) = 2(1) + 3 = 5.

Front

What is the sum of two functions f(x) and g(x)?

Back

The sum of two functions f(x) and g(x) is defined as (f + g)(x) = f(x) + g(x).

Front

If f(x) = x^2 and g(x) = x + 1, what is f(g(2))?

Back

g(2) = 2 + 1 = 3; f(g(2)) = f(3) = 3^2 = 9.

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each output (y-value) is associated with exactly one input (x-value).

Front

What is the difference between a function and a relation?

Back

A relation is a set of ordered pairs, while a function is a specific type of relation where each input has exactly one output.