9.2/9.3 Transformation Brett Solberg AHS ‘11-’12

Warm-up Test for all three types of symmetry 1) 2x4 + 3 = y2 Are the following functions even or odd? 3) f(x) = |3x| 4) f(x) = x + 1 𝑥 Have your completed HW out for a stamp

Today’s Agenda Practice Graphing Transformations in Functions y = x2 y = |x| x2 + y2 = 1 Transformations in Functions Vertical Shifts Horizontal Shifts Stretching Shrinking Announcements PTC EC CPT SLCC

Parabola Fill in x,y table for y=x2 x y -2 -1 1 2

Absolute Value Fill in x,y table for y=|x| x y -2 -1 1 2

Circle x2 + y2 = 1

Vertical Shifts Adding or subtracting numbers shifts the graph up or down. f(x) = x2 f(x) = x2 + 1 f(x) = x2 – 2

Horizontal Shifts Adding or subtracting numbers from x shifts the graph horizontally. y = |x| y = |x – 1| y = |x + 3|

Notes Example y = f(x) + 1 y = f(x) -2 y = f(x + 1) y = f(x – 2)

Notes Example y = x2 + 1 y = |x| - 3 y = (x – 2)2 y = (x – 1)2 - 2

Vertical Stretching y = c*f(x) multiply y coordinates by c if c > 1, vertical stretch if c < 1, vertical shrink if c is negative, the graph is reflected across the x-axis multiply y coordinates by c y = x2 y = 2x2 y = ½x2 y = -x2

Notes Example y = 2f(x) y = -f(x) y = 1 2 f(x) y = -3f(x)

Horizontal Stretching y = f(c*x) if c > 1 horizontal stretch if c <1 horizontal shrink if c is negative, the graph is reflected across the y-axis. multiply the x coordinates by c

Notes Example y = f(2x) y = f(½x) y = f(-x) y = f(-3x) y = f(2x) – 1

Homework 9.2 pg 393 #1-24 all 9.3 pg 398 #1 – 53 odd Use graph paper