Function Notation

Front

What is a function in mathematical terms?

Back

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

Front

What is the definition of a relation that is not a function?

Back

A relation is not a function if at least one input is associated with more than one output.

Front

How do you evaluate a function at a specific point, such as f(8)?

Back

To evaluate a function at a specific point, substitute the input value into the function's equation.

Front

Given the function f(x) = -3x + 3, what is f(0)?

Back

f(0) = -3(0) + 3 = 3.

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 do you determine the domain and range from a set of ordered pairs?

Back

The domain is found by listing all the first elements (x-values) of the ordered pairs, and the range is found by listing all the second elements (y-values).

Front

What is the vertical line test and how is it used to determine if a relation is a function?

Back

The vertical line test states that if a vertical line intersects a graph at more than one point, the relation is not a function.

Front

What does it mean for a function to be linear?

Back

A linear function is a function that can be graphically represented as a straight line, typically in the form f(x) = mx + b.

Front

What is the slope-intercept form of a linear function?

Back

The slope-intercept form is given by the equation f(x) = mx + b, where m is the slope and b is the y-intercept.