IB Mathematics Analysis and Approaches 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 $y=\frac{1}{2}\tan (3(x+1))-2$.

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