The diagram shows the graph of the sum of the functions $f(x)$ and $g(x)$ - HSC - SSCE Mathematics Extension 1 - Question 4 - 2022 - Paper 1
Question 4
The diagram shows the graph of the sum of the functions $f(x)$ and $g(x)$.
$y = f(x) + g(x)$
Which of the following best represents the graphs of both $f(x)$ and $... show full transcript
Worked Solution & Example Answer:The diagram shows the graph of the sum of the functions $f(x)$ and $g(x)$ - HSC - SSCE Mathematics Extension 1 - Question 4 - 2022 - Paper 1
Step 1
Identify the sum of the functions
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Answer
To determine the graphs of f(x) and g(x) from their sum, analyze the shape of the graph given for y=f(x)+g(x). The graph appears as a concave up parabola suggesting both f(x) and g(x) are likely positive values when summed.
Step 2
Analyze the graph options
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Answer
Review each option from A to D:
Option A: This shows a parabola above the x-axis. It could represent f(x), but not g(x).
Option B: Does not display a correct combination to sum up to a parabola.
Option C: Shows a cubic shape; it does not fit the criteria.
Option D: Represents two functions that can combine to produce the given parabola.
Based on this analysis, option A does not fit. The next possible candidate is D.
Step 3
Conclusion
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Answer
After careful evaluation, the correct option that best represents the graphs of both f(x) and g(x) is A.
