Functions and Function Notation

Front

What is a function?

Back

A function is a relation in which each input (x-value) is associated with exactly one output (y-value).

Front

How can you determine if a relation is a function?

Back

A relation is a function if no x-value is repeated with different y-values.

Front

What is function notation?

Back

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

Front

What does f(x) = -4x - 5 represent?

Back

It represents a linear function where the slope is -4 and the y-intercept is -5.

Front

How do you evaluate a function at a specific point?

Back

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

Front

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

Back

The output is 1, since f(-2) = -2 + 3 = 1.

Front

What is the significance of ordered pairs in determining functions?

Back

Ordered pairs (x, y) help identify whether a relation is a function by showing the relationship between inputs and outputs.

Front

What is the difference between a function and a non-function?

Back

A function has a unique output for each input, while a non-function may have multiple outputs for the same input.

Front

What does g(-4) + f(1) represent in function evaluation?

Back

It represents the sum of the outputs of the functions g and f evaluated at -4 and 1, respectively.

Front

What is the vertical line test?

Back

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