SOLUTION: The function g is related to aparent functions. g(x)= 1/2|x-4|-5 a. Find the parent function b. Describe the sequence of transformation (Select all that apply) -Vertical

Algebra ->  Rational-functions -> SOLUTION: The function g is related to aparent functions. g(x)= 1/2|x-4|-5 a. Find the parent function b. Describe the sequence of transformation (Select all that apply) -Vertical       Log On


   

Question 1118781: The function g is related to aparent functions.
g(x)= 1/2|x-4|-5
a. Find the parent function
b. Describe the sequence of transformation (Select all that apply)
-Vertical shrink
-Horizontal shrink
-Horizontal shift of 4 units to the left
-Horizontal shift of 4 units to the right
-Vertical shift of 5 units downward
Answer by greenestamps(13203) About Me  (Show Source):
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For clarity, there should be parentheses around the coefficient: (1/2)|x-4|-5.

a. The parent function is f(x) = |x|

b.
-Vertical shrink -- yes; the factor (1/2) shrinks the graph vertically.
-Horizontal shrink -- no. A horizontal shrink is the same as a vertical stretch; this function has a vertical shrink.
-Horizontal shift of 4 units to the left -- no. (see next item)
-Horizontal shift of 4 units to the right -- yes; "x-a" shifts the graph RIGHT a units
-Vertical shift of 5 units downward -- yes; the "-5" at the end shifts the graph down 5 (or "up -5")