Functions & Function Notation

Front

What is a function?

Back

A function is a relation where each input (x-value) has exactly one output (y-value).

Front

What is function notation?

Back

Function notation is a way to represent functions using symbols, typically written as f(x), where 'f' is the function name and 'x' is the input variable.

Front

How do you evaluate a function at a specific value?

Back

To evaluate a function at a specific value, substitute the value into the function's equation and simplify.

Front

What does f(-2) mean if f(x) = x + 3?

Back

It means to substitute -2 for x in the equation: f(-2) = -2 + 3 = 1.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a relation is a function; if a vertical line intersects the graph 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 for a relation to be not a function?

Back

A relation is not a function if at least one input (x-value) is associated with more than one output (y-value).

Front

How do you find the value of h(x) = 5 - 9x at x = 8?

Back

Substitute 8 into the equation: h(8) = 5 - 9(8) = 5 - 72 = -67.

Front

What is the significance of the x-value in a function?

Back

The x-value is the input of the function, which determines the corresponding y-value (output) based on the function's rule.