Answered: Describe the transformations from the…

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,...

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Related questions

Question

Describe the transformations from the parent function, and then graph

f(x)=-x^3-5x^2-2x+8

Vertex:

Domain:

Range:

x-intercept:

y-intercept:

increasing interval:

Decreasing interval:

End Behavior:

Expert Solution

Step 1: Transformation

To describe the transformations from the parent function f(x) = x^3, we'll need to identify how the given function f(x) = -x^3 - 5x^2 - 2x + 8 has been modified:

Reflection over the x-axis: The negative sign in front of the x^3 term (-x^3) reflects the graph of the parent function f(x) = x^3 over the x-axis.
Vertical compression: The coefficients of the x^3 and x^2 terms are both negative, indicating that the graph is vertically compressed compared to the parent.
Horizontal translation: The constant term (+8) implies a vertical translation of 8 units up.