Math Problem Statement

graph the equation yequals=StartRoot x minus 3 EndRootx−3

Solution

Here is the graph of the equation y=x3y = \sqrt{x - 3}. As shown, the graph starts at x=3x = 3, because the square root function requires x30x - 3 \geq 0, which means x3x \geq 3.

Would you like further details or have any questions?

Here are some related questions to explore:

  1. How does the graph change if we shift the equation by adding constants?
  2. What happens to the graph if we change the square root to a different root, like cube root?
  3. Can you express the domain and range of this function explicitly?
  4. How would you graph y=2x6y = \sqrt{2x - 6}?
  5. What is the derivative of y=x3y = \sqrt{x - 3} and how does it describe the slope of the graph?

Tip: Always consider the domain of a square root function when graphing, as it determines where the function is defined!

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Math Problem Analysis

Mathematical Concepts

Algebra
Functions
Square Root Function
Graphing

Formulas

y = √(x - 3)

Theorems

Domain and Range of Square Root Functions

Suitable Grade Level

Grades 9-11