Question

The graph of the function y = g(x) is shown below.

Determine the value of y for g(3)

What are the zeros of the function y = g(x)?

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Answer 1

Answer:

∣∣g(x)∣−1∣=21

∣g(x)∣−1=±21

∣g(x)∣=23 and ∣g(x)∣=21

g(x)=2±3 and g(x)=2±1

Hence ∣g(x)∣=21 and ∣g(x)∣=23.

Now consider the graph of y=∣g(x)∣.

If we draw a straight line parallel to x axis passing through y=21, we get 6 points where the straight line cuts the the graph of y=∣g(x)∣. Hence we get 6 solutions to the equation of ∣g(x)∣=0.5.

Now if we draw the a straight line passing through y=1.5 and parallel to x axis, then the straight line cuts the graph of y=∣g(x)∣ at exactly 2 points.

Hence ∣g(x)∣=1.5 has 2 solutions.

Therefore, in total we get 8 solutions.