Algebra Chapter 1 Quiz Review

Questions and Answers

What is the domain and range of the function 𝑓(𝑥) = 4 in interval notation?

Domain: $(-, ext{∞},, ext{∞})$; Range: $[4, 4]$.

Determine if the function 𝑔(𝑥) = \frac{x + 5}{4} is linear or nonlinear.

The function is linear.

Identify the type of symmetry for the function 𝑓(𝑥) = -3𝑥 + 𝑥 and explain your rationale.

The function is odd.

List the coordinates of the relative maximum and minimum for a graph with one maximum at (2, 5) and one minimum at (4, 1).

<p>Relative Maximum: (2, 5); Relative Minimum: (4, 1).</p> Signup and view all the answers

Describe the end behavior of the function 𝑓(𝑥) = -2𝑥^2 + 3 and what it implies about its graph.

<p>As $x \to \pm\text{∞}$, $f(x) \to -\text{∞}$.</p> Signup and view all the answers

Study Notes

Function Analysis

Identify domain and range in interval notation for functions.
Domain represents all possible input values (x), while range indicates all possible output values (f(x)).

Continuity

Determine if a function is continuous (no breaks or gaps) or discontinuous (interruptions present).

Linear vs Nonlinear Functions

A function is linear if it can be expressed in the form y = mx + b, where m and b are constants.
Examples for analysis:
- ( f(x) = 4 ): Constant function, linear.
- ( -2xy = 3 ): Represents a relation, nonlinear.
- ( g(x) = \frac{x + 5}{4} ): Linear function.

Intercepts Identification

Find x-intercepts (where y=0) and y-intercepts (where x=0) using provided data or table.

Symmetry Types

Determine symmetry for functions:
- Line symmetry around the y-axis (even).
- Point symmetry around the origin (odd).
- No symmetry present.

Even, Odd, or Neither

Assess if functions are:
- Even: ( f(-x) = f(x) )
- Odd: ( f(-x) = -f(x) )
- Neither: does not satisfy either condition.
Example functions to evaluate:
- ( f(x) = -3x + x: ) Analyze for evenness or oddness.
- ( g(x) = -4x + 2x - x: ) Check for symmetry conditions.
- ( h(x) = 5x + 6x: ) Review for properties.

Extrema Coordinates

Maximum(s): Highest point(s) on the graph.
Minimum(s): Lowest point(s) on the graph.
Relative Maximum(s): Peaks within a given interval.
Relative Minimum(s): Valleys within a given interval.

End Behavior

Describe behavior of functions as ( x ) approaches positive or negative infinity.
Key patterns include increasing, decreasing, or stabilizing at certain values.

Graph Sketching

Create graphical representations based on specified key features, ensuring to highlight elements like intercepts, symmetry, and extrema.

Description

This quiz serves as a review for Chapter 1 of Algebra, focusing on functions. Students will practice identifying domain and range, determining continuity, and classifying functions as linear or nonlinear. Use this quiz to reinforce your understanding of foundational concepts in algebra.