Functions and Relations Review

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 corresponding y-value.

Front

How do you write the equation of a line in function notation?

Back

The equation of a line in function notation is written as f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is the difference between a function and a relation?

Back

A relation is any set of ordered pairs, while a function is a specific type of relation where each input (x-value) is associated with exactly one output (y-value).

Front

How can you determine if a mapping is a function?

Back

A mapping is a function if no x-value is repeated in the mapping. If any x-value corresponds to more than one y-value, it is not a function.

Front

What does the vertical line test determine?

Back

The vertical line test is a method to determine if a graph represents a function. If any vertical line intersects the graph at more than one point, the graph is not a function.

Front

Given f(x) = 2x + 1, find f(3).

Back

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

Front

Translate the coordinate pair (2, 5) into function notation.

Back

f(2) = 5.

Front

What is the output of f(x) = x^2 when x = -4?

Back

f(-4) = (-4)^2 = 16.

Front

Is the set of points {(1, 2), (1, 3), (2, 4)} a function?

Back

No, because the x-value 1 is associated with two different y-values (2 and 3).

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.