List all possible rational zeros f(x) = 3x 5 -5x 2 +x+6

1/3,2/3,1,2,3,6,-1/3,-2/3,-1,-2,-3,-6

The horizontal asymptote equals zero when:

the degree of the numerator is less than the degree of the denominator

the degree of the numerator and denominator are equal

the degree of the numerator is greater than the degree of the denominator

Precalculus Midterm

Quiz

•

Mathematics

•

9th Grade - University

•

Practice Problem

•

Medium

•

CCSS

HSF.BF.B.3, HSF-IF.C.7D, HSF-IF.C.7C

+7

Standards-aligned

Amy Burdyn

Used 234+ times

FREE Resource

About this resource

This Precalculus Midterm assesses fundamental polynomial and rational function concepts appropriate for grades 11-12. The quiz comprehensively covers function evaluation, transformations, polynomial zeros and their multiplicities, factored forms, even and odd functions, rational function asymptotes, function composition, and complex zeros. Students must demonstrate mastery of algebraic manipulation, understanding of polynomial behavior, rational root theorem application, and the ability to analyze rational functions systematically. The questions require students to connect algebraic representations with graphical interpretations, evaluate composite functions, apply the conjugate root theorem for polynomials with real coefficients, and identify key features of rational functions including vertical and horizontal asymptotes. These skills represent the essential foundation students need before advancing to calculus, particularly in understanding function behavior and polynomial theory. Created by Amy Burdyn, a Mathematics teacher in US who teaches grade 9-13. This assessment serves as an excellent comprehensive review tool that can effectively gauge student readiness for advanced mathematical concepts. Teachers can utilize this quiz for formal midterm assessment, targeted review sessions focusing on polynomial and rational function mastery, or as a diagnostic tool to identify specific areas requiring remediation before moving to limits and derivatives. The variety of question types makes it ideal for formative assessment, allowing educators to pinpoint whether students struggle with computational skills, conceptual understanding, or the connection between algebraic and graphical representations. This quiz aligns with Common Core standards A-APR.2, A-APR.3, F-IF.7, F-BF.1, and F-IF.4, ensuring students develop the analytical skills necessary for success in calculus and higher-level mathematics courses.

19 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Find f(4) when f(x) = x²+5x-1

12

35

-35

24

Tags

CCSS.HSF.IF.A.2

2.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Write the equation of a function that has the given characteristics: the graph of y=x², shifted 6 units upward

y=x+6

y=x²-6

y=x²+6

y=(x²+6)+6

Tags

CCSS.HSF.BF.B.3

3.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Evaluate f(2)

5

-5

-3

0

Tags

CCSS.HSF.IF.A.2

4.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

This graph is _______ in the highlighted areas.

Decreasing

Increasing

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

5.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Given x=5, x =3/2, and x= 5/3...
which of the following is the correct factored form?

(x-5)(2x-3)(3x-5)

(x+5)(2x+3)(3x-5)

(x-5)(x-3/2)(x-5/3)

(x-5)(3x-2)(5x-3)

Tags

CCSS.HSA.APR.B.3

6.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

f(x)= x²(x – 2)³(x – 7)

Find and select each real zero and its multiplicity

0 (Mult of 2), 2 (Mult of 3), 7 (mult 1)

2 (Mult of 3), 7 (mult 1)

0, 2, 7

2 (mult of 2), 7 (mult of 3)

Tags

CCSS.HSF-IF.C.7C

7.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Find the zeros of the function and graph.
y=(x + 2)(x - 3)(3x - 5)

x=-2, x=3, x=5/3

x=2, x=-3, x=-3/5

x=2, x=-3, x=5/3

x=-2, x=3, x=5

Tags

CCSS.HSF-IF.C.7C

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Precalculus Midterm

19 questions

Find f(4) when f(x) = x²+5x-1

Write the equation of a function that has the given characteristics: the graph of y=x², shifted 6 units upward

Evaluate f(2)

This graph is _______ in the highlighted areas.

Given x=5, x =3/2, and x= 5/3...
which of the following is the correct factored form?

f(x)= x²(x – 2)³(x – 7)

Find and select each real zero and its multiplicity

Find the zeros of the function and graph.
y=(x + 2)(x - 3)(3x - 5)

List all possible rational zeros
f(x) = 3x⁵-5x²+x+6

Let f(x) = 3x^2 - 9x +2.
Is k = -3 a zero of the function?

Is the graph an even, odd, or neither function
f(x) = x² + 2

Access all questions and much more by creating a free account

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Precalculus Midterm

19 questions

Find f(4) when f(x) = x2+5x-1

Write the equation of a function that has the given characteristics: the graph of y=x2, shifted 6 units upward

Evaluate f(2)

This graph is _______ in the highlighted areas.

Given x=5, x =3/2, and x= 5/3...which of the following is the correct factored form?

f(x)= x2(x – 2)3(x – 7)Find and select each real zero and its multiplicity

Find the zeros of the function and graph.y=(x + 2)(x - 3)(3x - 5)

List all possible rational zerosf(x) = 3x5-5x2+x+6

Let f(x) = 3x^2 - 9x +2.Is k = -3 a zero of the function?

Is the graph an even, odd, or neither function f(x) = x2 + 2

Access all questions and much more by creating a free account

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Find f(4) when f(x) = x²+5x-1

Write the equation of a function that has the given characteristics: the graph of y=x², shifted 6 units upward

Given x=5, x =3/2, and x= 5/3...
which of the following is the correct factored form?

f(x)= x²(x – 2)³(x – 7)

Find and select each real zero and its multiplicity

Find the zeros of the function and graph.
y=(x + 2)(x - 3)(3x - 5)

List all possible rational zeros
f(x) = 3x⁵-5x²+x+6

Let f(x) = 3x^2 - 9x +2.
Is k = -3 a zero of the function?

Is the graph an even, odd, or neither function
f(x) = x² + 2