Question Type 4: Creating a description explaining function transformations Exercises

Describe the sequence of transformations applied to the graph of $y = x^3$ to obtain the graph of $y = -2(x - 1)^3 + 4$.

Describe the sequence of transformations applied to the graph of $y = \sqrt{x}$ to obtain the graph of $y = 2\sqrt{-x + 3} - 1$.

Describe the sequence of transformations applied to the graph of $y = e^x$ to obtain the graph of $y = 4e^{x - 2} - 1$.

Describe the sequence of transformations applied to the graph of $y = \sin x$ to obtain the graph of $y = 5\sin(2x - 6)$.

Describe the sequence of transformations applied to the graph of $y = x^2$ to obtain the graph of $y = (x - 3)^2 + 4$.

Describe the sequence of transformations applied to the graph of $y = |x|$ to obtain the graph of $y = -|x + 2| + 1$.

Describe the sequence of transformations applied to the graph of $y = \frac{1}{x}$ to obtain the graph of $y = \frac{3}{x + 2} - 5$.

Describe the sequence of transformations applied to the graph of $y = \ln x$ to obtain the graph of $y = \ln(2x + 4) + 5$.

Describe the sequence of transformations applied to the graph of $y = \cos x$ to obtain the graph of $y = -3\cos(2x) + 5$.

Given a function $y = f(x)$, describe the transformations applied to obtain $y = f(-x) + 3$.

Describe the sequence of transformations applied to the graph of $y = \tan x$ to obtain the graph of $y = \frac{1}{2}\tan\bigl(3(x + 1)\bigr) - 2$.

Describe the sequence of transformations applied to the graph of $y = \sin x$ to obtain the graph of $y = 2\sin\left(x - \frac{\pi}{4}\right)$.