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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 $f(x)$ a... 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 Graph Characteristics
Answer
First, analyze the graph given in the question. The graph represents the sum of two functions, and , where the sum is shown as convex and intersects the x-axis at one point. This suggests that at this point, one function is negative while the other is positive.
Step 2
Evaluate the Options
Answer
Next, examine each option:
- Option A: The graph depicts two positive slopes; this option cannot result in a sum that is zero.
- Option B: This option roughly follows the characteristics seen in the question's graph, with one function being below the x-axis and one above, indicating the overlap of negative and positive values.
- Option C: This graph does not have proper intersections and resembles a reflection rather than a sum; thus, it is incorrect.
- Option D: Similar to option C, it does not derive from the characteristics of the provided graph.
Through this assessment, Option B closely matches the conditions set forth by the original graph.
Step 3