Worksheet Key 1) (–∞, –4] 2) [–1, ∞) 3) (–4, ∞) 4) (–∞, –2) 5) (–∞, –5) 6) (–8, ∞) 7) (–36, ∞) 8) (–16, ∞) 9) (–∞, 6/5) 10) (4, ∞) 11) (–∞, 23/3) 12) (–74/7, ∞) 13) x > 75 14) x < 77 8/13/2019 10:15 AM Parent Functions

Quiz When done, turn in the quiz to the back and pick up a parent function chart and fill it out 8/13/2019 10:15 AM Parent Functions

8/13/2019 10:15 AM Parent Functions

Revised ©2014 Viet.dang@humble.k12.tx.us Parent Functions Revised ©2014 Viet.dang@humble.k12.tx.us 8/13/2019 10:15 AM Parent Functions

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: 8/13/2019 10:15 AM Parent Functions

Parent Functions Family Rule Constant f(x) = c Linear f(x) = x Quadratic f(x) = x2 Cubic f(x) = x3 Graph Table x –2 –1 1 2 y c x –2 –1 1 2 y x –2 –1 1 2 y 4 x –2 –1 1 2 y –8 8 Domain Range 8/13/2019 10:15 AM Parent Functions

Parent Functions Family Rule Square Root f(x) = √x Cubic Root Reciprocal/Rational f(x) = 1/x Absolute Value f(x) = |x| Exponential f(x) = 2x Graph Table x 1 4 9 y 2 3 x –8 –1 1 8 y –2 2 x –2 –1 1 2 y –.5 DNE .5 x –2 –1 1 2 y x –2 –1 1 2 y 1/4 1/2 4 Domain Range 8/13/2019 10:15 AM Parent Functions

Scale Factor (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. 8/13/2019 10:15 AM Parent Functions

Vertical Shifts of A For shifts of A of ax2 + bx + c = y, the bigger the A, the smaller the graph gets. 8/13/2019 10:15 AM Parent Functions

Vertical Shifts of C For shifts of C of ax2 + bx + c = y, the change of the C, the y–intercept shifts up or down 8/13/2019 10:15 AM Parent Functions

Horizontal Shifts ADDED, it moves to the LEFT 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 8/13/2019 10:15 AM Parent Functions

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 8/13/2019 10:15 AM Parent Functions

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Example 1 Given the graph of f(x) = x – 3, determine the domain, range, and transformation change in Interval Notation 8/13/2019 10:15 AM Parent Functions

Example 2 Given the graph of f(x) = 2x, determine the domain, range, and transformation change in Interval Notation 8/13/2019 10:15 AM Parent Functions

Your Turn Given the graph of f(x) = (1/2)x + 5, determine the domain, range, and transformation change in Interval Notation 8/13/2019 10:15 AM Parent Functions

Example 3 Given the graph of f(x) = (x + 1)2 – 3, determine the domain, range, and transformation change in Interval Notation 8/13/2019 10:15 AM Parent Functions

Example 4 Given the graph of f(x) = –|x – 2| + 4, determine the domain, range, and transformation change in Interval Notation 8/13/2019 10:15 AM Parent Functions

Example 5 Given the graph of f(x) = y = –2(x – 3)3 + 1, determine the domain, range, and transformation change in Interval Notation 8/13/2019 10:15 AM Parent Functions

Your Turn Given the graph of f(x) = (x – 1)2 – 4, determine the domain, range, and transformation change in Interval Notation 8/13/2019 10:15 AM Parent Functions

Example 6 Given a linear parent function, the shift of the equation is 4 units up, determine the equation. 8/13/2019 10:15 AM Parent Functions

Example 7 Given an absolute value parent function, the shift of the equation is 4 units down and 2 units to the left, determine the equation. 8/13/2019 10:15 AM Parent Functions

Your Turn Given a quadratic parent function, the shift of the equation is 3 units down and 4 units to the left, determine the equation. 8/13/2019 10:15 AM Parent Functions

Assignment Worksheet 8/13/2019 10:15 AM Parent Functions