From the curve y=|x|, draw (i) y=|x-1|+1 (ii) y=|x+1|-1 (iii) y=|x+2|-3.

Exercise 1.4 · Q7

y=|x|

(i)

y=|x-1|+1

(ii)

y=|x+1|-1

(iii)

y=|x+2|-3

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Step 1 (i) $y=|x-1|+1$ . This is $f(x-1)+1$ : shift RIGHT by 1 (since $x-1$ inside), then UP by 1. The V-vertex moves from $(0,0)$ to $(1,1)$ .

Step 2 (ii) $y=|x+1|-1$ . This is $f(x+1)-1$ : shift LEFT by 1, then DOWN by 1. Vertex moves from $(0,0)$ to $(-1,-1)$ .

Step 3 (iii) $y=|x+2|-3$ . This is $f(x+2)-3$ : shift LEFT by 2, then DOWN by 3. Vertex moves from $(0,0)$ to $(-2,-3)$ . …

Q.From the curve $y=|x|$ , draw