Consider the function shown - HSC - SSCE Mathematics Standard - Question 2 - 2024 - Paper 1
Question 2
Consider the function shown.
Which of the following could be the equation of this function?
A. y = 2x + 3
B. y = 2x - 3
C. y = -2x + 3
D. y = -2x - 3
Worked Solution & Example Answer:Consider the function shown - HSC - SSCE Mathematics Standard - Question 2 - 2024 - Paper 1
Step 1
Identify the characteristics of the function shown
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Answer
From the graph, the function appears to be a straight line crossing the y-axis and inclined downwards. The line likely has a negative slope, suggesting that it decreases as the x values increase.
Step 2
Analyze the given options
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Answer
Next, we check each equation:
A. y=2x+3 - This has a positive slope, which does not match our graph.
B. y=2x−3 - This also has a positive slope.
C. y=−2x+3 - This has a negative slope, which agrees with the graph's inclination.
D. y=−2x−3 - This has a negative slope as well, but the y-intercept (-3) is lower than the function shown in the graph.
Step 3
Determine the correct equation
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Answer
Among the options, equation C (y=−2x+3) represents a line with a negative slope that intersects the y-axis at a point higher than the graph, which seems plausible given the graph's appearance. Therefore, this is the best choice.
