Math Problem Statement

h(x)=-|x -6|+3 graph for me

Solution

Here is the graph of the function h(x)=x6+3h(x) = -|x - 6| + 3. The upside-down "V" shape represents the negative absolute value, with its vertex at (6,3)(6, 3).

Would you like a further explanation of this graph or how to interpret it?

Here are five related questions you might explore:

  1. What is the domain and range of h(x)=x6+3h(x) = -|x - 6| + 3?
  2. How does the vertex of an absolute value function shift when modifying its equation?
  3. How would the graph change if the function was h(x)=x6+3h(x) = |x - 6| + 3 instead?
  4. Can this graph represent any real-world situations? If so, which ones?
  5. How would you find the intercepts of this function?

Tip: The absolute value function creates symmetry, and when multiplied by a negative, it inverts vertically!

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Math Problem Analysis

Mathematical Concepts

Algebra
Absolute Value Functions
Transformations

Formulas

h(x) = -|x - 6| + 3

Theorems

Absolute Value Function Transformation
Vertex of Absolute Value Function

Suitable Grade Level

Grades 9-11