Homework Help is Here – Start Your Trial Now!
Math
Algebra
Consider the functions k(x) = x-1, mix) = x + 2, n(x)=x-3. and fox) = kon-mox-ND). a Graph k(x), m(x), and n(x). y₁ 8- Determine the degree of the function f(x). Explain your reasoning. Determine the zeros of fix). Explain your reasoning. Determine the y-intercept of f(x). Explain your reasoning. Sketch the graph of f(x). -8 -4 4 U -4 -8 4

Consider the functions k(x) = x-1, mix) = x + 2, n(x)=x-3. and fox) = kon-mox-ND). a Graph k(x), m(x), and n(x). y₁ 8- Determine the degree of the function f(x). Explain your reasoning. Determine the zeros of fix). Explain your reasoning. Determine the y-intercept of f(x). Explain your reasoning. Sketch the graph of f(x). -8 -4 4 U -4 -8 4

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
See similar textbooks
icon
Related questions
Question

please help with this practice problems! not a graded assignment!

 

# Polynomial Functions Practice ## 1. Consider the functions \(k(x) = x - 1\), \(m(x) = x + 2\), \(n(x) = x - 3\), and \(f(x) = k(x) \cdot m(x) \cdot n(x)\). **a.** Graph \(k(x)\), \(m(x)\), and \(n(x)\). **b.** Determine the degree of the function \(f(x)\). Explain your reasoning. **c.** Determine the zeros of \(f(x)\). Explain your reasoning. **d.** Determine the y-intercept of \(f(x)\). Explain your reasoning. **e.** Sketch the graph of \(f(x)\). ### Graph Explanation - The graph illustrated is a Cartesian plane with x- and y-axes marked. The function \( f(x) \) is a cubic polynomial formed by the product of three linear factors: \(k(x)\), \(m(x)\), and \(n(x)\). ## 2. Consider the graphs of the quadratic function \(g(x) = (x - 2)^2\) and the cubic function \(f(x) = g(x) \cdot h(x)\). **a.** Determine the degree of the function \(h(x)\). Explain your reasoning. **b.** Determine the x-intercept(s) of \(h(x)\). Explain your reasoning. ### Graph Explanation - The second graph on the right shows \(g(x)\) as a parabola opening upwards and intersects the x-axis at \(x = 2\). - The function \(f(x)\) is shown as a cubic curve intersecting at different points, indicating the combination of \(g(x)\) with another polynomial \(h(x)\). These exercises focus on understanding how polynomial functions are constructed and how their algebraic properties, such as degree and intercepts, can be determined and represented graphically.
Transcribed Image Text:# Polynomial Functions Practice ## 1. Consider the functions \(k(x) = x - 1\), \(m(x) = x + 2\), \(n(x) = x - 3\), and \(f(x) = k(x) \cdot m(x) \cdot n(x)\). **a.** Graph \(k(x)\), \(m(x)\), and \(n(x)\). **b.** Determine the degree of the function \(f(x)\). Explain your reasoning. **c.** Determine the zeros of \(f(x)\). Explain your reasoning. **d.** Determine the y-intercept of \(f(x)\). Explain your reasoning. **e.** Sketch the graph of \(f(x)\). ### Graph Explanation - The graph illustrated is a Cartesian plane with x- and y-axes marked. The function \( f(x) \) is a cubic polynomial formed by the product of three linear factors: \(k(x)\), \(m(x)\), and \(n(x)\). ## 2. Consider the graphs of the quadratic function \(g(x) = (x - 2)^2\) and the cubic function \(f(x) = g(x) \cdot h(x)\). **a.** Determine the degree of the function \(h(x)\). Explain your reasoning. **b.** Determine the x-intercept(s) of \(h(x)\). Explain your reasoning. ### Graph Explanation - The second graph on the right shows \(g(x)\) as a parabola opening upwards and intersects the x-axis at \(x = 2\). - The function \(f(x)\) is shown as a cubic curve intersecting at different points, indicating the combination of \(g(x)\) with another polynomial \(h(x)\). These exercises focus on understanding how polynomial functions are constructed and how their algebraic properties, such as degree and intercepts, can be determined and represented graphically.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps with 7 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education
SEE MORE TEXTBOOKS