warm up Find the zeros of the function

warm up • Find the zeros of the function • f(x) = 9 x 4 – 25 x 2

Linear Functions • Equation: Y = mx + b • Example: y = 3 x – 2 • Key characteristics: largest exponent 1

Quadratic function • Equation: y = ax 2 + bx + c • Example: y = 2 x 2 + 3 x – 5 • Key characteristics: largest exponent 2

Cubic function • Equation: y = ax 3 + bx 2 + cx + d • Example: y = -3 x 3 + 2 x 2 + 3 x – 5 • Key characteristics: largest exponent 3

Absolute Value function • Equation: y = |x - h | + k • Example: y = | x + 3| - 4 • Key characteristics: absolute value bars

Square Root function •

Reciprocal/ Rational function •

Exponential function • Equation: y = ax • Example: y = 2 x • Key characteristics: variable as an exponent

logarithmic function • Equation: y = logb x • Example: y = log 2 x • Key characteristics: logarithm

piecewise function f(x) = x 2 + 1 , x 0 x– 1, x 0

Step function greatest integer function • Equation: y = [|x|] • Example: y = [|2 x + 1|] • Key characteristics: greatest integer function symbol

Name the parent function from the graphs below.

Describe the shape of the equations below • f(x) = √(x) + 3 • f(x) = 1/(x-3) • f(x) = Ix-2 I • f(x) = 2 x 3 -3 • f(x) = [[x]] + 3

Describe the shape and equation of the following functions • Linear function • Square root function • Exponential function • Cubic function • Piecewise function • Reciprocal function • Step function • Quadratic function • Logarithmic function • Absolute value function

homework • Page 71 • 1 – 9 (all) , 57, 59, 61 • Page 80 • 27 – 41 (odd) a – c

Exploring transformations • ________ - a change in the position, size or shape of a figure. • A _________, or slide is a transformation that moves each point in a figure the same distance in the same direction.

Vertical and Horizontal translations • Vertical translation up h(x) = f(x) + c • Vertical translation down h(x) = f(x) – c • Horizontal translation right h(x) = f(x - c) • Horizontal translation left h(x) = f(x + c)

Vertical and horizontal translations

Vertical and horizontal translations • Describe the translations taking place • F(x) = |x + 3| • F(x) = |x| - 4 • F(x) = (x – 4)2 • F(x) = (x + 2)2 – 3

Identify the translation(s) taking place in the following functions • f(x) = x 2 + 3 • f(x) = (x - 4)2 • h(x) = (x+2)3 +1 • g(x) = √(x-3) +5

reflection • A reflection is a transformation that flips across a line called the line of reflection. • Reflection over the x-axis h(x) = -f(x) • Reflection over the y-axis h(x) = f(-x)

Reflecting graphs • Reflection over the y-axis • F(x)=(x-2)2 - 1 • F(x)=(-x-2)2 - 1 �Reflection over the x-axis �F(x)= x 2 �F(x)= -x 2

Describe the transformations taking place • F(x) = -|x + 2| - 3 • F(x) = (-x + 2)2 + 3 • F(x) = - (x + 2) • F(x) = |-x + 2|

Nonrigid Transformations Nonrigid transformations are those that cause a distortion—a change in the shape of the original graph. Vertical Stretch or shrink h(x) = cf(x) vertical stretch c > 1 vertical shrink 0 < c < 1 Horizontal Stretch or Shrink h(x) = f(cx) horizontal shrink c > 1 horizontal stretch 0 < c < 1

Example 4 – Nonrigid Transformations Compare the graph of each function with the graph of f (x) = | x |. a. h(x) = 3| x | b. g(x) = |x|

Example 4 – Nonrigid Transformations Compare the graph of each function with the graph of f (x) = x 2 a. h(x) = | 2 x | b. g(x) = | x |

Describe the transformation on the following functions • k(x) = ½ x 2 • f(x) = (9/4 x)3 – 7 • h(x) = 2√(x + 3) • g(x) = -(2 x - 5)2 + 4

homework • page 65 • 1 - 9 ( all) • page 73 • 21 - 29 (odd) • 47 and 49