Math Problem Statement

Use transformations of the standard cubic function, f(x) = x^3, to graph the function h(x) = -(x - 3)^3. What transformations are needed to graph the function h(x)?

Solution

The given function is h(x)=−(x−3)3h(x) = -(x - 3)^3, which is a transformation of the standard cubic function f(x)=x3f(x) = x^3.

Step-by-step transformation:

  1. Horizontal Shift: The term ( (

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Math Problem Analysis

Mathematical Concepts

Function transformations
Cubic functions
Graph reflections

Formulas

f(x) = a(x-h)^3 + k
Reflection across the x-axis: -f(x)

Theorems

Transformation Theorem: Horizontal shifts and reflections

Suitable Grade Level

Grades 10-12

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