Parent Functions and Transformations
Explore parent functions and their transformations including translations, reflections, stretches, and compressions at a Grade 12 level.
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Parent Functions and Transformations
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Read each question carefully and provide the best answer. Show all your work for short answer questions.
1. Which transformation maps the graph of y = x² to the graph of y = (x - 3)² + 5?
Shift left 3 units, shift up 5 units
Shift right 3 units, shift up 5 units
Shift left 3 units, shift down 5 units
Shift right 3 units, shift down 5 units
2. The graph of f(x) = |x| is reflected across the x-axis and then stretched vertically by a factor of 2. Which equation represents the new graph?
y = 2|x|
y = -2|x|
y = |-2x|
y = -|2x|
3. A horizontal stretch or compression of a function f(x) by a factor of 'c' results in the function f( ).
4. Reflecting a function f(x) across the y-axis yields the function g(x) = .
5. Describe the transformations applied to the parent function y = √x to obtain the graph of y = -√(x + 4) - 1.
6. The order of transformations (translations, reflections, stretches/compressions) does not affect the final graph of a function.
True
False
7. Graph the parent function f(x) = x³ and the transformed function g(x) = -(x - 2)³ + 1 on the coordinate plane below.