Functions

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What is the notation for a function?

Back

Functions are typically denoted by letters such as f, g, or h, followed by parentheses containing the input variable, e.g., f(x).

Front

What does it mean for h(x) = 0?

Back

It means we are looking for the value of x that makes the function h equal to zero.

Front

How do you find the rate of change of a function?

Back

The rate of change of a function can be found by calculating the difference in the output values divided by the difference in the input values, often represented as \( \frac{\Delta y}{\Delta x} \).

Front

What is the output of the function f(x) = 3x - 8 when x = 6?

Back

To find f(6), substitute 6 into the function: f(6) = 3(6) - 8 = 18 - 8 = 10.

Front

What is the vertical line test?

Back

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

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

What does it mean if a relation 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?

Back

To evaluate a function at a specific point, substitute the value of the input variable into the function and simplify.