The graph of the function $y = f(x)$ is shown - HSC - SSCE Mathematics Extension 2 - Question 4 - 2017 - Paper 1
Question 4
The graph of the function $y = f(x)$ is shown.
A second graph is obtained from the function $y = f(x)$.
Which equation best represents the second graph?
A. $y = \... show full transcript
Worked Solution & Example Answer:The graph of the function $y = f(x)$ is shown - HSC - SSCE Mathematics Extension 2 - Question 4 - 2017 - Paper 1
Step 1
A. $y = \sqrt{f(x)}$
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Answer
This equation would suggest that only the positive values of the original function are considered. The resulting graph would not maintain the original shape of the function as it would take the square root of the values, modifying the behavior around the x-axis.
Step 2
B. $y^2 = f(x)$
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This represents the relationship where the square of y equals the function. This could lead to a graph that reflects about the x-axis, which is not what the second graph depicts.
Step 3
C. $y = [f(x)]^2$
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This transformation takes the original function and squares its output. The resulting graph would change any negative outputs of f(x) to positive values while retaining the overall structure of the graph. Therefore, it aligns with the modifications shown in the second graph.
Step 4
D. $y = f(x^2)$
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This would compress the graph horizontally and could generate a different shape that does not match the transformation seen in the second graph.
