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:
This is a transformed version of the parent function .
Steps for Graphing
-
Start with the parent function :
- The graph of starts at the origin and increases slowly as increases.
-
Apply the horizontal shift:
The inside the square root shifts the graph to the left by 3 units. So instead of starting at , the graph now starts at . -
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 , the output -value is multiplied by 4 compared to the parent function.
Key Points:
- The graph starts at .
- As 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:
- What are the effects of horizontal and vertical shifts on any parent function?
- How does a vertical stretch or compression affect the shape of a graph?
- How do you find the domain and range of a transformed function?
- Can you describe how to graph the inverse of ?
- How would this transformation change if it were ?
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