Find the domain of the rational function f(x) = x/ ( x 2 -25)

(-∞, -5) U (-5, 5) U (5, ∞)

f ( x ) = 3 x − 2 f\left(x\right)=\frac{3}{x-2} f ( x ) = x − 2 3 Determine the vertical and horizontal asymptotes of the function.

horizontal: y = 0 vertical: x = 2

horizontal: y = -2 vertical: x = 2

horizontal: y = -2 vertical: x = 0

horizontal: y = 2 vertical: x = 0

Unit 2 Test - Analyzing Polynomial and Rational Functions

Authored by James Bryan

Mathematics

11th Grade

CCSS covered

Used 63+ times

Unit 2 Test - Analyzing Polynomial and Rational Functions

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This quiz comprehensively covers polynomial and rational function analysis, addressing core topics appropriate for grade 11 Algebra 2 or Pre-Calculus students. The questions systematically assess students' understanding of polynomial degree identification, end behavior analysis, intercept determination, extrema counting, domain and range concepts, and asymptote identification. Students need mastery of polynomial operations including factoring, synthetic division, and the Rational Root Theorem, along with sophisticated graphing skills to analyze function behavior. The rational function component requires understanding of vertical, horizontal, and oblique asymptotes, domain restrictions, and the relationship between numerator and denominator degrees. Advanced concepts include identifying holes in rational functions, determining function continuity, and constructing polynomial functions from given characteristics. Students must demonstrate both computational fluency and conceptual understanding of how algebraic properties translate to graphical behavior. Created by James Bryan, a Mathematics teacher in the US who teaches grade 11. This assessment serves as a comprehensive unit test that effectively evaluates student mastery of polynomial and rational function analysis through varied question formats and complexity levels. Teachers can utilize this quiz for summative assessment at the conclusion of a functions unit, as a comprehensive review before standardized testing, or as a diagnostic tool to identify specific areas requiring remediation. The progression from basic degree identification to complex asymptote analysis makes it suitable for differentiated instruction and scaffolded learning. This quiz aligns with Common Core standards A-APR.2, A-APR.3, A-APR.6, and F-IF.7 for polynomial operations and graphing, along with A-REI.2 and F-BF.3 for rational function analysis and transformation.

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25 questions

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MULTIPLE CHOICE QUESTION

10 mins • 1 pt

What is the degree of the polynomial function
P(x)=3x⁴- 7x²- 2x⁷- x + 4?

MULTIPLE CHOICE QUESTION

10 mins • 1 pt

Identify the end behavior:

The end behavior of the graph is x →∞, y→∞ and x→∞, y→⁻∞

The end behavior of the graph is x →∞, y→∞ and x→⁻∞, y→∞

The end behavior of the graph is x →∞, y→∞ and x→⁻∞, y→-∞

The end behavior of the graph is The end behavior of the graph is x →∞,y→⁻∞ and x→∞, y→⁻∞

Tags

CCSS.HSF-IF.C.7A

MULTIPLE CHOICE QUESTION

10 mins • 1 pt

Identify the end behavior:

The end behavior of the graph is x →∞, y→∞ and x→∞, y→⁻∞

The end behavior of the graph is x →∞, y→∞ and x→⁻∞, y→∞

The end behavior of the graph is x →∞, y→∞ and x→⁻∞, y→0

The end behavior of the graph is x →∞,y→∞and x→⁻∞, y→⁻∞

Tags

CCSS.HSA.REI.D.10

MULTIPLE CHOICE QUESTION

10 mins • 1 pt

Identify the x-intercepts:

No x-intercpts

x = -2, x = 3, x = -8

x = -2, x = 3

x = -2, x = 3, x = 8

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.B.4

CCSS.HSA.REI.D.11

MULTIPLE CHOICE QUESTION

10 mins • 1 pt

How many relative maximums does this function have?

Tags

CCSS.HSA.APR.B.3

MULTIPLE CHOICE QUESTION

10 mins • 1 pt

How many relative minimums does this function have?

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

MULTIPLE CHOICE QUESTION

10 mins • 1 pt

What are all the y-intercepts?

(0, -6.25)

(-3,0), (-2,0), (2,0), (3,0)

(0, 36)

(-∞, ∞)

Tags

CCSS.HSF-IF.C.7A

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Unit 2 Test - Analyzing Polynomial and Rational Functions

What is the degree of the polynomial function
P(x)=3x⁴- 7x²- 2x⁷- x + 4?

Identify the end behavior:

Identify the end behavior:

Identify the x-intercepts:

How many relative maximums does this function have?

How many relative minimums does this function have?

What are all the y-intercepts?

Identify the decreasing interval:

Is this an odd or even function?

A rational function can be written in the form

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Unit 2 Test - Analyzing Polynomial and Rational Functions

What is the degree of the polynomial function P(x)=3x4 - 7x2 - 2x7 - x + 4?

Identify the end behavior:

Identify the end behavior:

Identify the x-intercepts:

How many relative maximums does this function have?

How many relative minimums does this function have?

What are all the y-intercepts?

Identify the decreasing interval:

Is this an odd or even function?

A rational function can be written in the form

Access all questions and much more by creating a free account

Popular Resources on Wayground

Discover more resources for Mathematics

What is the degree of the polynomial function
P(x)=3x⁴- 7x²- 2x⁷- x + 4?