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 $g(... 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 Functions
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Answer
The graph provided shows the combined output of two functions f(x) and g(x), where the y-coordinate is the sum of their values at each point of x.
Step 2
Analyze Graph Options
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Answer
To determine the correct pair of functions, we need to analyze each option (A, B, C, D) to see which two functions can add together to form the given graph. Look for characteristics like intersections, peaks, and general curvature of the graphs.
Step 3
Select the Correct Graph
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Answer
Upon analysis, option A shows a parabolic curve that suggests two functions that, when summed, would produce the upward-opening graph shown in the original diagram. Thus, the best representation of f(x) and g(x) is option A.
