University:
High School
Course:
High School Mathematics
Academic year:

2022
Views:

253

Pages:

2
Author:

Cyncuncew7o63

Instructions: Write a function g whose graph represents the indicated transformation of the graph of f. Use graphing technology (graphing calculator, 1 desmos.com) to check your answer. 1. Problems and Solutions: Original Function: f(x) = |(1/3)x| Transformation: Translation 2 units to the left Solution: g(x) = |(1/3)(x + 2)| Original Function: f(x) = -|x + 9| - 1 Transformation: Translation 6 units down Solution: g(x) = -|x + 9| - 7 Original Function: f(x) = -2x + 2 Transformation: Translation 7 units down Solution: g(x) = -2x - 5 Original Function: f(x) = (1/2)x + 8 Transformation: Reflection in the x-axis Solution: g(x) = -(1/2)x - 8 Original Function: f(x) = 4 + |x + 1| Transformation: Reflection in the y-axis Solution: g(x) = 4 + |-x + 1| Original Function: f(x) = -5x Transformation: Vertical shrink by a factor of 1/5 Solution: g(x) = -x Original Function: f(x) = |x + 3| + 2 Transformation: Vertical stretch by a factor of 4 Solution: g(x) = 4|x + 3| + 8 NOTES Concept 6: Transformations of Parent Functions 1.2 Transformations of Linear & Absolute Value Functions A. TRANSFORMATION RULES - y = f(x + h) Horizontal Translation left hunits → y = f(x - h) Horizontal Translation right h units ↑ y = f(x) + k Vertical Translation up k units 1 y = f(x) - k Vertical Translation down k units y = - f(x) Reflection in x-axis y = f(- x) Reflection in y-axis y = af(x) Vertical Stretch by a factor ofa a > 1 Vertical Shrink by a factor of a if 0 < a < 1 y = f(ax) Horizontal Stretch by a factor 1/a if 0 < a < 1 reciprocal Horizontal Shrink by a factor of if a > 1