Math Problem Statement
write down the transformations implied by sqrt(x+2)+3. find the x transformation, y transformation, and the parent function
Solution
The function can be analyzed in terms of transformations applied to its parent function.
1. Parent Function:
The parent function here is .
2. Transformations:
-
X-Transformation (Horizontal Shift):
- The term indicates a horizontal shift.
- Since the expression is , it implies a left shift by 2 units.
- Transformation: .
-
Y-Transformation (Vertical Shift):
- The term outside the square root indicates a vertical shift.
- It implies a shift upwards by 3 units.
- Transformation: .
Summary:
- Parent Function:
- Horizontal Shift: Left by 2 units.
- Vertical Shift: Up by 3 units.
This means the function is obtained by shifting the graph of the parent function 2 units to the left and 3 units up.
Would you like a detailed graph of this transformation or have any further questions?
5 Related Questions:
- How does the graph of compare to ?
- What happens to the domain and range of the function after the transformation?
- How would the function change if the transformation was ?
- Can you derive the inverse function of ?
- What would be the effect of a vertical stretch by a factor of 2 on the function?
Tip:
When dealing with horizontal shifts, remember that adding a value inside the function moves the graph to the left, while subtracting moves it to the right.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Algebra
Function Transformations
Square Root Functions
Formulas
f(x) = sqrt(x + 2) + 3
Horizontal shift: x' = x - (-2)
Vertical shift: y' = y + 3
Theorems
-
Suitable Grade Level
Grades 9-11
Related Recommendation
Transforming the Square Root Function: 2√x Shifted Up 3 and Left 5
Square Root Function Transformations: f(x) = sqrt(x - 2) - 4
Square Root Function Shifted Right and Up: g(x) = 4√(x - 3) + 3
Function Transformation: Reflection, Vertical Shift, and Horizontal Shift Applied to Square Root Function
Graph and Describe the Square Root Function f(x) = √(x + 4) - 3