Functions & Relations

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 in the domain, there is one and only one corresponding y-value.

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

How can you determine if a relation is a function?

Back

A relation is a function if no two ordered pairs have the same first element (x-value) with different second elements (y-values).

Front

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

Back

f(2) = 2(2) + 3 = 4 + 3 = 7.

Front

What does f(0) represent in a function?

Back

f(0) represents the y-intercept of the function, which is the value of the function when the input x is 0.

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, then the curve is not a function.

Front

If f(x) = -3x + 3, what is the slope of the function?

Back

The slope of the function f(x) = -3x + 3 is -3.

Front

What is an example of a function?

Back

An example of a function is f(x) = x^2, where each input x has a unique output x^2.

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line, typically in the form f(x) = mx + b, where m is the slope and b is the y-intercept.