Question

Sketch a graph y = |x – 3| – 2 and describe the translations.

I don't understand this at all

Answer 1

Start with y = | x |
you should be able to graph this
if not, look at Wolfram:
http://www.wolframalpha.com/input/?i=y+%3D+%7Cx%7C

a big V with nothing below the x-axis

consider: y = |x| - 2 , we just moved the entire graph down 2 units.
http://www.wolframalpha.com/input/?i=y+%3D+%7Cx%7C+-+2

Now we will do a horizontal shift of 3 units to the <b>right</b>
y = |x-3| - 2

http://www.wolframalpha.com/input/?i=y+%3D+%7Cx-3%7C+-+2

or all in 1 graph:
http://www.wolframalpha.com/input/?i=plot+y+%3D+%7Cx%7C,+y+%3D+%7Cx%7C+-+2+,+y+%3D+%7Cx-3%7C+-+2

in general, if
y = f(x)
then f(x + a) will move f(x) a units to the left
then f(x - a) will move f(x) a units to the right

then f(x) + b , will move f(x) b units up
then f(x) - b , will move f(x) b units down

can you see how I applied these rules to your equation ?

Answer 2

Use only the positive(absolute) value of the results inside the brackets. The student should do P5 and P6, and use the six points for graphing. The sketch will resemble a parabola that opens upward.
Y = |x-3| - 2.
Y = |0-3| - 2 = 3 - 2 = 1. P1(0,1).
Y = |1-3| - 2 = 2 - 2 = 0. P2(1,0).
Y = |2-3| - 2 = 1 - 2 = -1. P3(2,-1).
Y = |3-3| - 2 = 0 - 2 = -2. P4(3,-2).
Y = |4-3| - 2 = ? - 2 = ? P5(4,?).
Y = |5-3| - 2 = ? - 2 = ? P6(?, ?).