Pre-Calculus Function Intro Practice

If $x = 4$, what is the possible value of $y$?

What is the output when the input is 3?

If $x = 0$, what is a possible answer for $y$?

Which of the following graphs could represent a function?

What is the possible value of $y$ when $x = 1$?

What defines a function based on a set of ordered pairs?

In the scenario where the amount of candy collected depends on the number of doors knocked, which variable is independent?

If the input of a function is the time of day since midnight, what does the output represent?

Which of the following statements is true regarding the relationship between the amount of candy eaten and the number of cavities the following year?

What does the output represent when the input is the height in centimeters of a specific individual?

How would you classify the relationship that determines the average high temperature based on the month of the year?

Which of these pairs exemplifies a relationship that does not represent a function?

What would be the effect of increasing the number of doors knocked on the number of candies collected?

Function Identification

A relationship represents a function if each input (independent variable) has exactly one output (dependent variable).
Example scenarios include identifying functions based on ordered pairs, considering domain and range.

Independent and Dependent Variables

Independent variable: Determines the value of the dependent variable.
Examples:
- Candy collected while Trick-or-Treating depends on the number of doors knocked (independent: doors knocked).
- Candy eaten relates to the number of cavities the following year (independent: candy eaten).
- Ability to draw quality art is affected by the hours spent drawing (independent: hours spent).
- Month of the year influences average high temperature (independent: month).

Interpretations of Inputs in Functions

Inputs can represent various metrics and their corresponding outputs:
- Time since midnight relates to the number of cars in a parking lot.
- Height in centimeters correlates to a weight output in pounds.
- Number of lame jokes shared connects to irritability levels of students.

Graphing and Table Methods

Techniques for determining values from a graph include using a tracing method or function notation.
Values inferred from graphs may require approximation if lying between integers.

Graph Analysis for Function Representation

Graphs should be assessed for vertical line test: a vertical line should not intersect the graph more than once for it to be considered a function.
Analyze given graphs to ascertain function status based on this criterion.

Output Calculation

Understanding specific inputs to find outputs often involves substitutions into mathematical expressions or functions.

This quiz focuses on identifying functions from given relationships. You will evaluate independent and dependent variables, domain, range, and ordered pairs. Complete each question to demonstrate your understanding of functions.