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Algebra 1: Functions and Graph Analysis

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Questions and Answers

Why is the given relation in Problem 3 classified as a function?

It has at least one input with multiple outputs.

It has more outputs than inputs.

Each input has exactly one output. (correct)

It contains both linear and non-linear relationships.

For graph b in Problem 4, which statement about the intervals of increase and decrease is correct?

The graph is increasing for -1 < x < 3. (correct)

The graph is increasing when x is greater than 3.

The graph is decreasing for all values of x.

The graph does not have any intervals of increase.

What x-intercepts are observed in graph c?

(0, 0)

(-5, 0)

(-2, 0)

(4, 0) (correct)

What can be inferred about the behavior of the function shown in graph a?

The function begins to decrease after x = -2. Signup and view all the answers

Which of the following best describes the outputs of the relation in Problem 3?

Each output corresponds to one input. Signup and view all the answers

Is the graph in Exercise 1a a function?

Yes, it is a function. Signup and view all the answers

What is the domain type for the graph in Exercise 1b?

Continuous Signup and view all the answers

What are the y-intercept and x-intercept for the graph in Exercise 2b?

y-intercept (0, -3), x-intercept (-1, 0) & (3, 0) Signup and view all the answers

In which interval is the graph in Exercise 2b increasing?

x > 1 Signup and view all the answers

What is the range of the graph in Exercise 1c?

{1, 3, 4, 5} Signup and view all the answers

Study Notes

Determining if a Relation is a Function

A relation is a function if each input value corresponds to exactly one output value.

Analyzing a Graph

The x-intercept is the point where the graph crosses the x-axis.
The y-intercept is the point where the graph crosses the y-axis.
A graph is increasing when the y-value increases as the x-value increases.
A graph is decreasing when the y-value decreases as the x-value increases.

Discrete and Continuous Domains

A discrete domain consists of separate, distinct values, often represented as a set of numbers.
A continuous domain includes all values within a given range, often represented using inequalities.

Worksheet Examples

Nancy Rajoub completed a math worksheet on November 14th, 2004, in Algebra 1 CPA during Period 4.

Function Examples

Exercise 1: Graphs are analyzed for whether they represent functions, and their domain and range are identified.
- The domain is the set of possible input values.
- The range is the set of possible output values.
Exercise 2: Graphs' x-intercepts, y-intercepts, increasing intervals, and decreasing intervals are determined from the graphs.

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Description

Test your understanding of functions and their properties in Algebra 1. This quiz covers determining if a relation is a function, analyzing graphs, and understanding discrete versus continuous domains. Practice your skills with real worksheet examples and exercises.