Math Problem Statement
Solution
Let's break down and answer each part of the problem from the images you've uploaded.
Original Function:
1. Reflection across the x-axis:
When reflecting a function across the x-axis, we multiply the entire function by . This gives:
So, the correct choice is:
2. Shift left by 2 units:
To shift a function left by units, replace with . In this case, shifting left by 2 units means replacing with , giving:
So, the correct choice is:
3. Shift down by 1 unit:
To shift a function down by units, subtract from the entire function. For a downward shift of 1 unit:
So, the correct choice is:
4. Shift right by 2 units and up by 1 unit:
To shift a function right by units, replace with , and to shift up by units, add to the entire function. So, shifting right by 2 and up by 1 gives:
So, the correct choice is:
5. Vertical stretch by a factor of 3:
To stretch a function vertically by a factor of , multiply the entire function by . For a vertical stretch by 3:
So, the correct choice is:
Would you like further details on these transformations or any other questions about the problems? Here are some additional practice questions you can consider:
- How do you reflect a function across the y-axis?
- What is the effect of a horizontal stretch on ?
- How would you describe the transformation ?
- What happens to the domain and range after a vertical stretch of ?
- How do transformations affect the intercepts of a function?
Tip: Always apply horizontal transformations (like shifts or stretches) inside the function's argument and vertical ones outside.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Function Transformations
Square Root Functions
Algebra
Formulas
Reflection across x-axis: f(x) = -f(x)
Horizontal shift: f(x - h) (right) or f(x + h) (left)
Vertical shift: f(x) + k (up) or f(x) - k (down)
Vertical stretch: a * f(x), where a > 1 for stretching
Theorems
-
Suitable Grade Level
Grades 9-12
Related Recommendation
Transformations and Reflections of Square Root Function y = √x
Square Root Function Transformations: Shifting, Stretching, and Reflecting
Transform the Square Root Function y = sqrt(x) to Match Another Function
Graph Transformations: Convert y = 3 + 2√(4 - x) to y = -√x + 6
Understanding Function Transformations of the Square Root Function