Relations and Functions

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 the vertical line test?

Back

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

Front

What is the definition of a relation in mathematics?

Back

A relation is a set of ordered pairs, where each pair consists of an input (x) and an output (y).

Front

How do you evaluate a function at a specific point?

Back

To evaluate a function at a specific point, substitute the given input value into the function's equation and simplify to find the output.

Front

What does it mean for a relation to be a function?

Back

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

Front

If f(x) = -4x + 5, what is f(0)?

Back

f(0) = 5.

Front

If g(x) = x^2 + x, what is g(-4)?

Back

g(-4) = 12.

Front

What is a mapping diagram?

Back

A mapping diagram visually represents a relation by showing how each input is paired with its corresponding output.

Front

Can a function have repeating x-values?

Back

Yes, a function can have repeating x-values as long as each x-value corresponds to only one y-value.

Front

What is the output of f(-2) if f(x) = x^2 + 3?

Back

f(-2) = 7.