Math Problem Statement

y=

x−3∣

Solution

The equation you've provided is:

y=x3y = |x - 3|

This represents an absolute value function. The absolute value function outputs the positive version of any value inside it, regardless of whether it's positive or negative.

For this function:

  • When x3x \geq 3, y=x3y = x - 3
  • When x<3x < 3, y=(x3)=3xy = -(x - 3) = 3 - x

The graph of this function is V-shaped and has its vertex at the point (3,0)(3, 0).

Would you like a detailed explanation on graphing or solving it for specific values of xx?

Related Questions:

  1. What is the graph of y=x3y = |x - 3|?
  2. How do you solve x3=0|x - 3| = 0?
  3. What are the properties of absolute value functions?
  4. How can you find the range of y=x3y = |x - 3|?
  5. How would you modify the equation if there was a coefficient outside the absolute value?

Tip:

Remember, absolute value functions always yield non-negative outputs!

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Math Problem Analysis

Mathematical Concepts

Algebra
Absolute Value Functions

Formulas

y = |x - 3|
y = x - 3 when x >= 3
y = 3 - x when x < 3

Theorems

Absolute Value Theorem

Suitable Grade Level

Grades 6-8