Lake Zurich High School Parent Graphs with translations By: Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org Last Updated: November 21, 2005

y =|x| Jeff Bivin -- LZHS

y = |x+1| + 2 x+1 = 0 x = -1 2 1 Jeff Bivin -- LZHS

y = |2x+5| - 4 2x+5 = 0 x = -(5/2) 4 5/2 squeeze squeeze Slope: -2 Jeff Bivin -- LZHS

y = 2 |x - 3| + 1 x - 3 = 0 x = 3 1 3 stretch stretch Slope: 2 Jeff Bivin -- LZHS

y = 3 |2x - 3| - 4 2x - 3 = 0 x = 3/2 4 stretch stretch 3/2 squeeze Slope: -3(2) = -6 Slope: 3(2) = 6 Jeff Bivin -- LZHS

y = [ x ] x = 0 1 1 Note: y = x Length = 1/1 = 1 Start: (0, 0) Height = 1 Note: y = x Jeff Bivin -- LZHS

y = [ x+1] + 2 x+1 = 0 1 1 x = -1 1 2 Note: y = (x + 1) + 2 y = x + 3 Length = 1/1 = 1 1 Start: (-1, 2) Height = 1 2 Note: y = (x + 1) + 2 y = x + 3 Jeff Bivin -- LZHS

y = 3[(½)x] stretch stretch stretch stretch Note: y = 3( (1/2)x ) Length = 1/(1/2) = 2 stretch stretch Height = 3 Start: (0, 0) stretch stretch Note: y = 3( (1/2)x ) y = (3/2)x Jeff Bivin -- LZHS

y = -2[ x+1]+3 1 x+1 = 0 x = -1 1 stretch stretch 3 Note: Length = 1/1 = 1 Start: (-1, 3) 1 Height = -2 stretch stretch 3 Note: y = -2(x + 1) + 3 y = -2x + 1 Jeff Bivin -- LZHS

y = [ |x| ] Jeff Bivin -- LZHS

y = | [x] | y = [ x ] Jeff Bivin -- LZHS

y = | [x] | y = | x | Jeff Bivin -- LZHS

f(x) = x2 Jeff Bivin -- LZHS

f(x) = (x - 3)2 + 1 x - 3 = 0 x = 3 3 1 Jeff Bivin -- LZHS

f(x) = (x + 2)2 - 4 x + 2 = 0 x = -2 2 4 Jeff Bivin -- LZHS

f(x) = 2(x - 3)2 - 1 x - 3 = 0 x = 3 3 1 stretch stretch Jeff Bivin -- LZHS

Jeff Bivin -- LZHS

x - 2 = 0 x = 2 3 2 Jeff Bivin -- LZHS

x + 3 = 0 x = -3 3 4 Jeff Bivin -- LZHS

f(x) = x3 Jeff Bivin -- LZHS

f(x) = (x-4)3 - 2 x - 4 = 0 x = 4 4 2 Jeff Bivin -- LZHS

f(x) = -(x + 2)3 -1 x + 2 = 0 flip x = -2 2 1 Jeff Bivin -- LZHS

Jeff Bivin -- LZHS

x - 4 = 0 x = 4 y = 2 4 2 x = 4 Jeff Bivin -- LZHS

x + 2 = 0 y = 3 x = -2 2 3 x = -2 Jeff Bivin -- LZHS

flip x - 3 = 0 x = 3 y = 1 3 1 x = 3 Jeff Bivin -- LZHS

f(x) = 2x Jeff Bivin -- LZHS

f(x) = 2x-3 x - 3 = 0 x = 3 (3, 1) 3 Jeff Bivin -- LZHS

f(x) = 2x+2 - 3 x + 2 = 0 x = -2 3 2 y = -3 (-2, -2) Jeff Bivin -- LZHS

f(x) = 2-x (0, 1) Jeff Bivin -- LZHS

f(x) = -(2)-x+4 – 2 -x + 4 = 0 x = 4 4 2 y = -2 flip (4, -3) Jeff Bivin -- LZHS

y = g(x) Jeff Bivin -- LZHS

y = g(x-3) - 2 x - 3 = 0 x = 3 3 2 Jeff Bivin -- LZHS