4.7: Transformations of Linear Functions Do Now Determine the constant of variation to the following equations: 3x – y = 0 2) Suppose y varies directly as x, and y = 16 when x = 12. Find x when y = 20. 3) As you watch a movie, 24 individual pictures or frames flash a screen (s) each second. Create an equation y where s is screen. 12/25/2018 10:42 PM 4.7: Transformations of Linear Functions

4.7: Transformations of Linear Functions 12/25/2018 10:42 PM 4.7: Transformations of Linear Functions

Transformations of Functions Section 4.7 12/25/2018 10:42 PM 4.7: Transformations of Linear Functions

4.7: Transformations of Linear Functions Equations Slope Equation: 12/25/2018 10:42 PM 4.7: Transformations of Linear Functions

4.7: Transformations of Linear Functions Recall Slope Y-intercept 12/25/2018 10:42 PM 4.7: Transformations of Linear Functions

Transformations of Functions The parent function equation of a linear function is y = x. The equation of a line using Slope-Intercept form is y = mx + b where m is the slope and b is the y-intercept The change is slope or m does change in size. The larger the m, the steeper it gets. The smaller the m, the flatter it gets. It does not matter whether the m is positive or negative. The change of the y-intercept or b does not change in size. It changes in location. 12/25/2018 10:42 PM 4.7: Transformations of Linear Functions

4.7: Transformations of Linear Functions Recall Graph y = x 12/25/2018 10:42 PM 4.7: Transformations of Linear Functions

4.7: Transformations of Linear Functions Example 1 Graph y = x + 3 and compare to y = x x Process Column y –2 –1 1 2 1 2 3 4 5 The y-intercept shifts up 3 spots from the parent function 12/25/2018 10:42 PM 4.7: Transformations of Linear Functions

4.7: Transformations of Linear Functions Example 2 Graph y = x – 4 and compare to y = x The y-intercept shifts down 4 spots from the parent function 12/25/2018 10:42 PM 4.7: Transformations of Linear Functions

4.7: Transformations of Linear Functions Example 3 Graph y = 2x and compare to y = x x Process Column y –2 –1 1 2 –1 –2 2 4 12/25/2018 10:42 PM 4.7: Transformations of Linear Functions

4.7: Transformations of Linear Functions Example 3 Graph y = 2x and compare to y = x The slope of y = 2x is 2 times steeper than y = x 12/25/2018 10:42 PM 4.7: Transformations of Linear Functions

4.7: Transformations of Linear Functions Example 4 Graph y = 1/2x and compare to y = x x Process Column y –2 –1 1 2 –1 –1/2 ½ 1 The slope of y = 1/2x is 1/2 times flatter than y = x 12/25/2018 10:42 PM 4.7: Transformations of Linear Functions

Graphing Calculator Ex 3 and 4 Graph y = 2x and compare to y = x 12/25/2018 10:42 PM 4.7: Transformations of Linear Functions

4.7: Transformations of Linear Functions Example 5 Draw the function from the parent function y = x and the y-intercept moves up 4 spaces 12/25/2018 10:42 PM 4.7: Transformations of Linear Functions

4.7: Transformations of Linear Functions Your Turn Draw the function from the parent function y = x and the y-intercept moves down 5 spaces 12/25/2018 10:42 PM 4.7: Transformations of Linear Functions

4.7: Transformations of Linear Functions Example 6 Draw the function from the parent function y = x and the slope is 2 times the original function 12/25/2018 10:42 PM 4.7: Transformations of Linear Functions

4.7: Transformations of Linear Functions Example 7 Draw the function from the parent function y = x and the slope is 1/2 times the original function 12/25/2018 10:42 PM 4.7: Transformations of Linear Functions

4.7: Transformations of Linear Functions Example 8 Draw the function from the parent function y = x and the slope is 1/3 times the original function, reflected 12/25/2018 10:42 PM 4.7: Transformations of Linear Functions

4.7: Transformations of Linear Functions Your Turn Draw the function from the parent function y = x and the slope is 4 times the original function 12/25/2018 10:42 PM 4.7: Transformations of Linear Functions

4.7: Transformations of Linear Functions Example 9 Draw the function from the parent function y = x and the slope is 5 times the original function and moves down 2 up from the y-intercept 12/25/2018 10:42 PM 4.7: Transformations of Linear Functions

4.7: Transformations of Linear Functions Example 10 Draw the function from the parent function y = x and the slope is 1/4 times the original function and moves down 3 down from the y-intercept. 12/25/2018 10:42 PM 4.7: Transformations of Linear Functions

4.7: Transformations of Linear Functions Your Turn Draw the function from the parent function y = x and the slope is 2/5 times the original function reflected and moves up 1 down from the y-intercept. 12/25/2018 10:42 PM 4.7: Transformations of Linear Functions

4.7: Transformations of Linear Functions Function Notation Known as “short-hand” writing f(x) does NOT mean f times x, it is known as “f is a function of x” When x is given, plug the equation in and solve Simplify 12/25/2018 10:42 PM 4.7: Transformations of Linear Functions

4.7: Transformations of Linear Functions Example 11 Given f(x) = x – 3, determine f(2). (2)2 f(2) = 4 – 3 f(2) = 1 12/25/2018 10:42 PM 4.7: Transformations of Linear Functions

4.7: Transformations of Linear Functions Example 12 Given f(x) = 2x – 10, determine f(6). 12/25/2018 10:42 PM 4.7: Transformations of Linear Functions

4.7: Transformations of Linear Functions Your Turn Given f(x) = –4x + 12, determine f(–8). 12/25/2018 10:42 PM 4.7: Transformations of Linear Functions

4.7: Transformations of Linear Functions Example 13 Given f(x) = 2x – 5, find the value of x so that f(x) = 15. 15 12/25/2018 10:42 PM 4.7: Transformations of Linear Functions

4.7: Transformations of Linear Functions Your Turn Given f(x) = 4x + 3, find the value of x so that f(x) = –13. 12/25/2018 10:42 PM 4.7: Transformations of Linear Functions

4.7: Transformations of Linear Functions Assignment Worksheet 12/25/2018 10:42 PM 4.7: Transformations of Linear Functions