Absolutely absolute

Algebra Level 3

Below is the graph of y = f ( x ) y=f(x) :

Match the following graphs with the correct equations:

  • y 1 = f ( ∣ x ∣ ) y_1=f(|x|)
  • y 2 = ∣ f ( x ) ∣ y_2=|f(x)|
  • y 3 = ∣ f ( − x ) ∣ y_3=|f(-x)|
  • y 4 = ∣ f ( ∣ x ∣ ) ∣ y_4=|f(|x|)|

Graph A

Graph B

Graph C

Graph D

A : y 1 , B : y 3 , C : y 2 , D : y 4 A: y_1, B: y_3, C: y_2, D: y_4 A : y 3 , B : y 4 , C : y 1 , D : y 2 A: y_3, B: y_4, C: y_1, D: y_2 A : y 1 , B : y 2 , C : y 4 , D : y 3 A: y_1, B: y_2, C: y_4, D: y_3 A : y 4 , B : y 3 , C : y 2 , D : y 1 A: y_4, B: y_3, C: y_2, D: y_1 A : y 1 , B : y 2 , C : y 3 , D : y 4 A: y_1, B: y_2, C: y_3, D: y_4 A : y 3 , B : y 4 , C : y 4 , D : y 1 A: y_3, B: y_4, C: y_4, D: y_1

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Wee Xian Bin by Wee Xian Bin , 25, Singapore

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1 solution

Julian Yu
Dec 22, 2018

y 1 : y_1: reflects the part of the graph to the right of the y-axis along the y-axis. This is shown by graph A.

y 2 : y_2: reflects the part of the graph that was below the x-axis along the x-axis. This is shown by graph B.

y 3 : y_3: reflects the entire graph along the y-axis, then reflects the part of the graph that was below the x-axis along the x-axis. This is shown by graph C.

y 4 : y_4: reflects the part of the graph to the right of the y-axis along the y-axis, then reflects the part of the graph that was below the x-axis along the x-axis. This is shown by graph D.

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