Math Problem Statement

y=√x-6

Solution

The equation you've provided is:

y=x6y = \sqrt{x} - 6

This describes a transformation of the square root function y=xy = \sqrt{x}. Here's how:

  1. Parent Function: The base function is y=xy = \sqrt{x}, which starts at the point (0,0)(0, 0) and gradually increases as xx increases.
  2. Vertical Shift: The entire graph of y=xy = \sqrt{x} is shifted 6 units downwards because of the subtraction of 6.

Key Points:

  • Domain: Since x\sqrt{x} is only defined for non-negative xx, the domain is x0x \geq 0.
  • Range: Since the square root of any number is non-negative and the graph is shifted down by 6, the range is y6y \geq -6.

If you want to sketch the graph, it would start at the point (0,6)(0, -6) and gradually rise as xx increases.

Would you like more details or have any questions?

Related Questions:

  1. How do we find the inverse of y=x6y = \sqrt{x} - 6?
  2. What are the intercepts of the graph of y=x6y = \sqrt{x} - 6?
  3. How does the function behave as xx \to \infty?
  4. Can we express the equation in terms of a piecewise function?
  5. How can we apply transformations to the graph y=x6y = \sqrt{x} - 6?

Tip: The square root function is non-linear, so shifts impact the graph differently than for linear functions like y=xy = x.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Square Root Function
Function Transformations

Formulas

y = √x
y = √x - 6

Theorems

Function Transformation Theorem

Suitable Grade Level

Grades 9-10