Essential Question: How do you write and sketch an equation of a function based on the parent graph? Students will write a comparison of the equation of the parent function and the equation of any of its children. Shifting, Reflecting and Stretching Graphs (Section 1-4)

Essential Question: How do you write and sketch an equation of a function based on the parent graph? Students will write a comparison of the equation of the parent function and the equation of any of its children. Section 1.4, Figure 1.40, Graphs of Common Functions pg 42

Essential Question: How do you write and sketch an equation of a function based on the parent graph? Students will write a comparison of the equation of the parent function and the equation of any of its children. Transformation: shifts, stretches, shrinks, and reflections of a parent graph.

Essential Question: How do you write and sketch an equation of a function based on the parent graph? Students will write a comparison of the equation of the parent function and the equation of any of its children. Section 1.4, Graphs of Vertical and Horizontal Shifts pg 43

Essential Question: How do you write and sketch an equation of a function based on the parent graph? Students will write a comparison of the equation of the parent function and the equation of any of its children. Section 1.4, Definitions of Vertical and Horizontal Shifts pg 43

Essential Question: How do you write and sketch an equation of a function based on the parent graph? Students will write a comparison of the equation of the parent function and the equation of any of its children. Compare the graph of each function with the graph of f(x) = x 3 Example 1 g(x) = x 3 -1 Example 2 h(x) = (x-1) 3 Example 3 k(x) = (x+2) 3 +1

Essential Question: How do you write and sketch an equation of a function based on the parent graph? Students will write a comparison of the equation of the parent function and the equation of any of its children. Find the equation for each function. (Hint the parent function is f(x) = x 2.) Example 4Example 5

Essential Question: How do you write and sketch an equation of a function based on the parent graph? Students will write a comparison of the equation of the parent function and the equation of any of its children. Section 1.4, Reflections in the Coordinate Axes pg 45

Essential Question: How do you write and sketch an equation of a function based on the parent graph? Students will write a comparison of the equation of the parent function and the equation of any of its children. Example 6 The graph of f(x) = x 4 is shown below. Find an equation for each of the following functions. a) b)

Essential Question: How do you write and sketch an equation of a function based on the parent graph? Students will write a comparison of the equation of the parent function and the equation of any of its children. Compare the graph of each function with the graph of Example 7 Example 8 Example 9

Essential Question: How do you write and sketch an equation of a function based on the parent graph? Students will write a comparison of the equation of the parent function and the equation of any of its children. Rigid vs. Nonrigid Transformations Rigid Transformations: horizontal shifts, vertical shifts and reflections, which leave the basic shape of the graph unchanged. Only the position is changed. Nonrigid Transformations: are those that cause a distortion (a change in the shape of the original graph.) Vertical StretchHorizontal Stretch Vertical ShrinkHorizontal Shrink

Essential Question: How do you write and sketch an equation of a function based on the parent graph? Students will write a comparison of the equation of the parent function and the equation of any of its children. Compare the graph of each function with the graph of Example 10 Example 11

Essential Question: How do you write and sketch an equation of a function based on the parent graph? Students will write a comparison of the equation of the parent function and the equation of any of its children. Compare the graph of each function with the graph of Example 12 Example 13 Example 14

Essential Question: How do you write and sketch an equation of a function based on the parent graph? Students will write a comparison of the equation of the parent function and the equation of any of its children. HW #62 pg (1-13 odd, odd)

Essential Question: How do you write and sketch an equation of a function based on the parent graph? Students will write a comparison of the equation of the parent function and the equation of any of its children. Sketch the graphs of the three functions by hand on the same rectangular coordinate system. Example 15

Essential Question: How do you write and sketch an equation of a function based on the parent graph? Students will write a comparison of the equation of the parent function and the equation of any of its children. Sketch the graphs of the three functions by hand on the same rectangular coordinate system. Example 16

Essential Question: How do you write and sketch an equation of a function based on the parent graph? Students will write a comparison of the equation of the parent function and the equation of any of its children. Sketch the graphs of the three functions by hand on the same rectangular coordinate system. Example 17

Essential Question: How do you write and sketch an equation of a function based on the parent graph? Students will write a comparison of the equation of the parent function and the equation of any of its children. Example 18 Use a graphing utility to graph the three functions in the same viewing window. Describe the graphs of g and h relative to the graph of f.

Essential Question: How do you write and sketch an equation of a function based on the parent graph? Students will write a comparison of the equation of the parent function and the equation of any of its children. Identify the parent function and describe the transformation shown in the graph. Write an equation for the graphed function. Example 19

Essential Question: How do you write and sketch an equation of a function based on the parent graph? Students will write a comparison of the equation of the parent function and the equation of any of its children. Identify the parent function and describe the transformation shown in the graph. Write an equation for the graphed function. Example 20

Essential Question: How do you write and sketch an equation of a function based on the parent graph? Students will write a comparison of the equation of the parent function and the equation of any of its children. (same instructions as #43-55) g is related to one of the six parent functions. (a) Identify the parent function. (b) Describe the sequence of transformations from f to g. (c) Sketch the graph of g by hand. (d) Use function notation to write g in terms of the parent function. Example 21

Essential Question: How do you write and sketch an equation of a function based on the parent graph? Students will write a comparison of the equation of the parent function and the equation of any of its children. (same instructions as #43-55) g is related to one of the six parent functions. (a) Identify the parent function. (b) Describe the sequence of transformations from f to g. (c) Sketch the graph of g by hand. (d) Use function notation to write g in terms of the parent function. Example 22

Essential Question: How do you write and sketch an equation of a function based on the parent graph? Students will write a comparison of the equation of the parent function and the equation of any of its children. HW #63 pg49 – 50 (15-19 odd, odd, all, 69-73odd) Pg #15-19 odd, #43-55 odd, #65, 67