3.4: Graphs and Transformations Worksheet Key 11/23/2018 10:30 PM 3.4: Graphs and Transformations 1

3.4: Graphs and Transformations Page 76 3) 5) 7) 9) 11) 13) 15) 17) 19) 21) 23) 24) 35) 37) 39) 11/23/2018 10:30 PM 3.4: Graphs and Transformations 2

3.4: Graphs and Transformations 11/23/2018 10:30 PM 3.4: Graphs and Transformations

3.4: Graphs and Transformations Quiz 11/23/2018 10:30 PM 3.4: Graphs and Transformations 4 4

Parent Functions and Transformations 11/23/2018 10:30 PM 3.4: Graphs and Transformations

What is a parent function? A. The parent function is the simplest function with the defining characteristics of the family. Functions in the same family are transformations of their parent function. B. There are main parent functions that are utilized through Algebra. They are the following: 11/23/2018 1-9 Parent Functions 6 6

3.4: Graphs and Transformations Parent Functions Family Rule Constant f(x) = c Linear Quadratic Cubic f(x) = x f(x) = x2 f(x) = x3 Graph Domain All Real Numbers All Real Numbers All Real Numbers All Real Numbers Range All Real Numbers All Real Numbers y > 0 All Real Numbers 11/23/2018 10:30 PM 3.4: Graphs and Transformations

3.4: Graphs and Transformations Parent Functions Family Rule Squ Root f(x) = √x Cubic Root f(x) = 3√x Reciprocal f(x) = 1/x Squ Root Exponential f(x) = √x f(x) = 2x Abs Value f(x) = |x| Graph Domain x > 0 All Real Numbers x ≠ 0 All Real Numbers [0, ∞) All Real Numbers Range y > 0 All Real Numbers y ≠ 0 y > 0 y > 0 11/23/2018 10:30 PM 3.4: Graphs and Transformations

3.4: Graphs and Transformations Scalar The equation will now look like, y = a(x – h) + k _h_ stands for the Horizontal Shift _k_ stands for the Vertical Shift The standard points will now be adjusted by the scalar (a) Multiply a with the x-values of the standard points. The scalar does not affect the new origin. 11/23/2018 10:30 PM 3.4: Graphs and Transformations

3.4: Graphs and Transformations Vertical Shifts of A For shifts of A of ax2 + bx + c = y, the bigger the A, the smaller the graph gets. 11/23/2018 10:30 PM 3.4: Graphs and Transformations

3.4: Graphs and Transformations Vertical Shifts of C For shifts of A of ax2 + bx + c = y, the change of the C, the y-intercept shifts up or down 11/23/2018 10:30 PM 3.4: Graphs and Transformations

3.4: Graphs and Transformations Horizontal Shifts For shifts of A of f(x)= a(x - h)2 + k, the change of the h, the graph shifts either left or right If the equation is… ADDED, it moves to the LEFT SUBTRACTED, it moves to the RIGHT 11/23/2018 10:30 PM 3.4: Graphs and Transformations

3.4: Graphs and Transformations Reflection Shifts For horizontal shifts of f(x)= –a(x - h)2 + k or others, the change of the a, the graph shifts reflects on the axis 11/23/2018 10:30 PM 3.4: Graphs and Transformations

Aerobic Exercises

Dance Moves…

3.4: Graphs and Transformations Example 1 Given the graph of f(x) = x – 3, determine the domain, range, and transformation change 11/23/2018 10:30 PM 3.4: Graphs and Transformations 16 16

3.4: Graphs and Transformations Example 2 Given the graph of f(x) = 2x, determine the domain, range, and transformation change 11/23/2018 10:30 PM 3.4: Graphs and Transformations 17 17

3.4: Graphs and Transformations Your Turn Given the graph of f(x) = 1/2x + 5, determine the domain, range, and transformation change 11/23/2018 10:30 PM 3.4: Graphs and Transformations 18 18

3.4: Graphs and Transformations Example 3 Given the graph of f(x) = 2(x + 1)2 – 3, determine the domain, range, and transformation change 11/23/2018 10:30 PM 3.4: Graphs and Transformations

3.4: Graphs and Transformations Your Turn Given the graph of y = –2(x – 3)3 + 1, determine the domain, range, and transformation change 11/23/2018 10:30 PM 3.4: Graphs and Transformations

3.4: Graphs and Transformations Assignment Worksheet 11/23/2018 10:30 PM 3.4: Graphs and Transformations