Kuta Software - Infinite Precalculus - Graphs of Polynomial Functions - Worksheets - 02

Oct 8, 2026

Uploaded by jayni

Worksheets for Infinite Precalculus focused on graphing polynomial functions. For each given function, tasks require finding real zeros and their multiplicities, identifying x-intercepts that cross the x-axis versus those that do not, and sketching the resulting graph. Additional questions ask students to describe end behavior using limits as x approaches positive and negative infinity, then apply critical-thinking prompts to construct polynomial functions satisfying specified zeros, values, and degree constraints.

LanguageEnglish

CategoryExam

FormatPDF

Pages4

Reading Time10 min

AccessFree to download

For each function

Real zeros and multiplicity

x-intercepts: crosses vs. doesn't cross

Sketch the graph

Describe end behavior

Critical thinking questions

Construct a polynomial from zeros and conditions

Construct a polynomial passing through given points

Kuta Software-Infinite Precalculus Graphs of Polynomial Functions Name Date Period For each function: (1) determine the real zeros and state the multiplicity of any repeated zeros,(2) list the x-intercepts where the graph crosses the x-axis and those where it does not cross the x-axis, and (3) sketch the graph. 1) f (x) 􀀠 􀀐x 􀀖 2) f (x) 􀀠 􀀕x 􀀖 􀀐 􀀖 x 􀀕 3) f (x) 􀀠 x 􀀗 􀀎 x 􀀖 􀀐 􀀗x 􀀕 􀀐 􀀗x 4) f (x) 􀀠 x 􀀗 􀀎 x 􀀖 5) f (x) 􀀠 􀀐x 􀀖 􀀎 􀀙x 􀀕 􀀐 􀀔􀀕x 􀀎 􀀛 6) f (x) 􀀠 x 􀀖 􀀐 􀀕x 􀀕 Describe the end behavior of each function. 7) f (x) 􀀠 􀀐x 􀀘 􀀎 􀀕x 􀀖 􀀐 x 􀀎 􀀔 8) f (x) 􀀠 􀀕x 􀀕 􀀐 􀀗x 􀀐 􀀖 9) f (x) 􀀠 x 􀀗 􀀐 􀀕x 􀀕 􀀐 x 􀀎 􀀔 10) f (x) 􀀠 􀀐x 􀀖 􀀐 􀀜x 􀀕 􀀐 􀀕􀀗x 􀀐 􀀕􀀓 11) f (x) 􀀠 􀀐x 􀀘 􀀎 􀀖 x 􀀖 􀀎 􀀔 12) f (x) 􀀠 x 􀀕 􀀎 􀀙x 􀀎 􀀙 Critical thinking questions: 13) Write a polynomial function f with the 14) Write a polynomial function g with degree following properties: greater than one that passes through the (a) Zeros at 􀀔 , 􀀕 , and 􀀖 points (􀀓 􀀔) (􀀔 􀀔), and (􀀕 􀀔) .(b) f (x) 􀁤 􀀓 for all values of x , , , ,(c) Degree greater than 1 Kuta Software-Infinite Precalculus Graphs of Polynomial Functions Name Date Period For each function: (1) determine the real zeros and state the multiplicity of any repeated zeros,(2) list the x-intercepts where the graph crosses the x-axis and those where it does not cross the x-axis, and (3) sketch the graph. 1) f (x) 􀀠 􀀐x 􀀖 2) f (x) 􀀠 􀀕x 􀀖 􀀐 􀀖 x 􀀕 Real zeros: 􀁞􀀓 mult. 3􀁠 x-int, crosses: 􀀓 x-int, doesn't cross: None Real zeros: 􀁞 􀀓 mult. 2, ~~ ~~􀀖􀀕 􀁠 x-int, crosses: 􀀖􀀕 x-int, doesn't cross: 􀀓 3) f (x) 􀀠 x 􀀗 􀀎 x 􀀖 􀀐 􀀗x 􀀕 􀀐 􀀗x 4) f (x) 􀀠 x 􀀗 􀀎 x 􀀖 Real zeros: 􀁞􀀓 , 􀀕 , 􀀐􀀕 , 􀀐􀀔􀁠 x-int, crosses: 􀀓 , 􀀕 , 􀀐􀀕 , 􀀐􀀔 x-int, doesn't cross: None Real zeros: 􀁞􀀓 mult. 3, 􀀐􀀔􀁠 x-int, crosses: 􀀓 , 􀀐􀀔 x-int, doesn't cross: None 5) f (x) 􀀠 􀀐x 􀀖 􀀎 􀀙x 􀀕 􀀐 􀀔􀀕x 􀀎 􀀛 Real zeros: 􀁞􀀕 mult. 3􀁠 x-int, crosses: 􀀕 x-int, doesn't cross: None 6) f (x) 􀀠 x 􀀖 􀀐 􀀕x 􀀕 Real zeros: 􀁞􀀓 mult. 2, 􀀕􀁠 x-int, crosses: 􀀕 x-int, doesn't cross: 􀀓 Describe the end behavior of each function. 7) f (x) 􀀠 􀀐x 􀀘 􀀎 􀀕x 􀀖 􀀐 x 􀀎 􀀔 8) f (x) 􀀠 􀀕x 􀀕 􀀐 􀀗x 􀀐 􀀖 lim f (x) 􀀠 􀁦 lim f (x) 􀀠 􀁦 xlf (x) 􀀠 􀀐􀁦 xlf (x) 􀀠 􀁦 x􀁯 􀁦 x􀁯 􀁦 9) f (x) 􀀠 x 􀀗 􀀐 􀀕x 􀀕 􀀐 x 􀀎 􀀔 10) f (x) 􀀠 􀀐x 􀀖 􀀐 􀀜x 􀀕 􀀐 􀀕􀀗x 􀀐 􀀕􀀓 lim f (x) 􀀠 􀁦 lim f (x) 􀀠 􀁦 xlf (x) 􀀠 􀁦 xlf (x) 􀀠 􀀐􀁦 x􀁯 􀁦 x􀁯 􀁦 11) f (x) 􀀠 􀀐x 􀀘 􀀎 􀀖 x 􀀖 􀀎 􀀔 12) f (x) 􀀠 x 􀀕 􀀎 􀀙x 􀀎 􀀙 lim f (x) 􀀠 􀁦 lim f (x) 􀀠 􀁦 xlf (x) 􀀠 􀀐􀁦 xlf (x) 􀀠 􀁦 x􀁯 􀁦 x􀁯 􀁦 Critical thinking questions: 13) Write a polynomial function f with the following properties: (a) Zeros at 􀀔 , 􀀕 , and 􀀖(b) f (x) 􀁤 􀀓 for all values of x (c) Degree greater than 1 f (x) 􀀠 􀀐(x 􀀐 􀀔)􀀕 􀂘 (x 􀀐 􀀕)􀀕 􀂘 (x 􀀐 􀀖)􀀕 14) Write a polynomial function g with degree greater than one that passes through the points (􀀓 , 􀀔), (􀀔 , 􀀔), and (􀀕 , 􀀔) . g(x) 􀀠 x(x 􀀐 􀀔)(x 􀀐 􀀕) 􀀎 􀀔 Create your own worksheets like this one with Infinite Precalculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)

FAQs

What must be determined for each polynomial function before graph sketching?

Determine the real zeros and the multiplicity of any repeated zeros, then list x-intercepts where the graph crosses the x-axis and where it does not cross it.

How are x-intercepts categorized in these worksheets?

x-intercepts are split into those where the graph crosses the x-axis and those where it does not cross the x-axis.

What does the worksheet require for end behavior?

Students describe end behavior using limits of f(x) as x approaches positive and negative infinity for each function.

Oct 8, 2026

Uploaded by jayni