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

What is a relation?

Back

A relation is a set of ordered pairs, where each pair consists of an input (x) and an output (y). A relation can be a function if it meets the criteria of having one output for each input.

Front

How can you determine if a mapping is a function?

Back

A mapping is a function if no x-value is paired with more than one y-value. You can use the vertical line test on a graph to check this.

Front

What is the vertical line test?

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, then the graph is not a function.

Front

Evaluate the function: f(x) = 2x + 3, find f(4).

Back

f(4) = 2(4) + 3 = 8 + 3 = 11.

Front

What does f(x) mean?

Back

f(x) is read as 'f of x' and represents the output of the function f for a given input x.

Front

Is the graph of y = x^2 a function?

Back

Yes, the graph of y = x^2 is a function because each x-value has exactly one corresponding y-value.

Front

Is the graph of y = ±√x a function?

Back

No, the graph of y = ±√x is not a function because each positive x-value corresponds to two y-values (one positive and one negative).

Front

Evaluate the function: f(x) = x - 5, find f(9).

Back

f(9) = 9 - 5 = 4.

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.