Question
Which of the following functions describe the graph shown in the below figure?
Options :
π¦ = ||π₯| + 1| β 2
π¦ = ||π₯| β 1| β 1
π¦ = ||π₯| + 1| β 1
π¦ = ||π₯ β 1| β 1|
Answer :
π¦ = ||π₯| β 1| β 1
Solution :
From the given graph,
When x = 0, y = 0
x = Β±1, y = -1
x = Β±2, y = 0
x = Β±3, y = 0
Now, let check the given options for the values of x = 0, Β±1, Β±2, Β±3
For x = 0:
y = ||x| + 1| β 2 = -1 (fails)
y = ||x| β 1| β 1 = 0
y = ||x| + 1| β 1 = 0
y = ||x β 1| β 1| = 0
For x = Β±1:
y = ||x| β 1| β 1 = -1
y = ||x| + 1| β 1 = 1 (fails)
y = ||x β 1| β 1| = 1 (fails)
For x = Β±2:
y = ||x| β 1| β 1 = 0
For x = Β±3:
y = ||x| β 1| β 1 = 1
Only y = ||x| β 1| β 1 satisfies the given graph
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