Final answer:
The function f(x)=x² can be transformed by reflecting over the y-axis, translating along the x-axis, stretching vertically, and compressing horizontally.
Step-by-step explanation:
The given function is f(x) = x². Let's analyze the effects of the transformations represented by g:
a) Reflection over the y-axis: This transformation is represented by the function f(-x). So, g(x) = f(-x) = (-x)² = x². Thus, there is no change in the graph of the function.
b) Translation along the x-axis: This transformation is represented by the function f(x - d), where d represents the amount of translation. If g(x) = f(x - 2), then g(x) = (x - 2)² = x² - 4x + 4. The graph of g(x) will be shifted 2 units to the right.
c) Vertical stretch: This transformation is represented by multiplying the function by a constant. If g(x) = 3f(x), then g(x) = 3(x²) = 3x². The graph of g(x) will be stretched vertically by a factor of 3.
d) Horizontal compression: This transformation is represented by multiplying the x-values of the function by a constant. If g(x) = f(kx), where k is the compression factor, then g(x) = (kx)² = k²x². The graph of g(x) will be compressed horizontally.