Functions & Relations

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input from a set of inputs.

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

Evaluate f(5) if f(x) = 3x - 8.

Back

f(5) = 3(5) - 8 = 15 - 8 = 7.

Front

For what value of x does f(x) = -2 if f(x) = 3x - 8?

Back

Set 3x - 8 = -2. Solving gives x = 2.

Front

What is the notation for a function?

Back

Functions are often denoted as f(x), g(x), etc., where 'f' or 'g' is the name of the function and 'x' is the input variable.

Front

What does it mean for a function to be linear?

Back

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

Front

What is the slope of the line represented by the function f(x) = 2x + 3?

Back

The slope is 2, which indicates the line rises 2 units for every 1 unit it moves to the right.

Front

What is the y-intercept of the function f(x) = 3x - 5?

Back

The y-intercept is -5, which is the point where the line crosses the y-axis.

Front

How do you find the x-intercept of a function?

Back

To find the x-intercept, set f(x) = 0 and solve for x.