Math Problem Statement

Graph the equation shown below by transforming the given graph of the parent function. y, equals, 4, square root of, x, plus, 3, end square root y=4 x+3 ​

x y x y Answer Attempt 1 out of 2

Solution

It seems like you're asking for the graph of a transformed square root function. However, your input may have some formatting issues. I will interpret your equation based on standard transformations and write it as:

y=4x+3y = 4\sqrt{x + 3}

This is a transformed version of the parent function y=xy = \sqrt{x}.

Steps for Graphing

  1. Start with the parent function y=xy = \sqrt{x}:

    • The graph of y=xy = \sqrt{x} starts at the origin (0,0)(0, 0) and increases slowly as xx increases.
  2. Apply the horizontal shift:
    The +3+3 inside the square root shifts the graph to the left by 3 units. So instead of starting at (0,0)(0, 0), the graph now starts at (3,0)(-3, 0).

  3. Apply the vertical stretch:
    The factor of 4 outside the square root stretches the graph vertically by a factor of 4. This means for each value of xx, the output yy-value is multiplied by 4 compared to the parent function.

Key Points:

  • The graph starts at (3,0)(-3, 0).
  • As xx increases, the graph rises faster due to the vertical stretch of 4.

Would you like me to graph this equation for you or provide further details?

Here are five related questions:

  1. What are the effects of horizontal and vertical shifts on any parent function?
  2. How does a vertical stretch or compression affect the shape of a graph?
  3. How do you find the domain and range of a transformed function?
  4. Can you describe how to graph the inverse of y=x+3y = \sqrt{x + 3}?
  5. How would this transformation change if it were y=4x+3y = -4\sqrt{x + 3}?

Tip: Always pay attention to signs inside and outside of a function when transforming a graph—positive values stretch, and negative values reflect or shift!

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Math Problem Analysis

Mathematical Concepts

Algebra
Function Transformations
Square Root Functions

Formulas

y = a√(x + b)
Parent function: y = √x

Theorems

Transformation Theorem
Vertical Stretch and Horizontal Shift Theorem

Suitable Grade Level

Grades 9-11