Porisma

A hint to get started

Transform a piecewise curve and crop to the requested interval

(i) State transformations taking y=x2y=x^2 to y=14(x−3)2y=\frac14(x-3)^2.

Define

f(x)={1,0≤x≤1,14(x−3)2,1<x≤3,0,otherwise.f(x)=\begin{cases}1,&0\le x\le1,\\ \frac14(x-3)^2,&1<x\le3,\\0,&\text{otherwise}.\end{cases}

(ii) Sketch f for −1≤x≤4.

(iii) Separately sketch y=1+f(x/2)y=1+f(x/2) for −1≤x≤4.

[2015/I/5]

CJC · Discussion · Question 9

Apply the transformations to each piece, then enforce the requested viewing interval.

Read the worked solution