Features of Functions + Function Algebra

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, and h, followed by parentheses containing the input variable, e.g., f(x).

Front

What does f(3) mean?

Back

f(3) represents the output of the function f when the input is 3.

Front

How do you evaluate f(x) = x^2 at x = 3?

Back

To evaluate f(3), substitute 3 into the function: f(3) = 3^2 = 9.

Front

What is function addition?

Back

Function addition involves adding the outputs of two functions for the same input: (f + g)(x) = f(x) + g(x).

Front

If f(x) = x^2 and g(x) = x + 3, what is (f + g)(3)?

Back

(f + g)(3) = f(3) + g(3) = 9 + 6 = 15.

Front

What is the concept of velocity in relation to functions?

Back

Velocity is the rate of change of position with respect to time, often represented as the derivative of a position function.

Front

What does it mean when velocity is decreasing?

Back

Velocity is decreasing when the derivative of the position function is negative, indicating that the position is changing at a slower rate.

Front

What is an increasing interval in a function?

Back

An increasing interval is a range of x-values where the function's output values are rising as x increases.

Front

What is a maximum height in the context of a function?

Back

The maximum height is the highest point on the graph of a function, often found at the vertex of a parabola.