Function Notation Overview and Evaluation

Which is true regarding the function f(x) given by the set of ordered pairs {(8, -3), (0, 4), (1, -5), (2, -1), (-6, 10)}?

What does v(r) represent in the function v(r) = 4/3πr^3?

Which equation must be true regarding the function if the point (-3, -5) is on its graph?

If point (4, 5) is on the graph of a function, which equation must be true?

How can the function represented by 9x + 3y = 12 be written using function notation with x as the independent variable?

What does t represent in the height function h(t) = -16t^2 + 32t + 10?

For which x is f(x) = -3?

What is f(5) in the given function table?

Which is true regarding the graphed function f(x)?

Function Notation Overview

The function f(x) has specific values for certain inputs based on ordered pairs such as f(-6) = 10.
The volume function v(r) calculates the volume of a basketball using the formula v(r) = (4/3)πr^3, where r is the radius.

Function Values and Graphs

If a point (-3, -5) lies on the graph, it indicates that f(-3) = -5.
The point (4, 5) confirms that f(4) = 5.

Converting Equations to Function Notation

The equation 9x + 3y = 12 can be represented in function notation as f(x) = -3x + 4.
A rocket's height can be modeled by h(t) = -16t² + 32t + 10, where t represents the number of seconds since the rocket was released.

Function Evaluation

In cases where a function is represented by a table, f(x) values can be directly identified, such as f(x) = -3 when x = -7, and f(5) = -8.
For the graphed function f(x), key points include f(5) = -1.

Characteristics of Graphed Functions

Specific values from function g(x):
- g(0) = 0
- g(1) = 1
- g(-1) = 1

General Insights

Understanding function notation and how to interpret values and graphs is crucial in analyzing mathematical relationships.
Functions often relate independent variables to dependent values through specific equations, tables, or graphs.

This quiz covers essential concepts of function notation, evaluation, and graph characteristics. It includes examples of converting equations to function notation and interpreting ordered pairs. Test your understanding of various functions and their graphical representations.