The graph of a cubic function, y = f(x), is given below - HSC - SSCE Mathematics Extension 1 - Question 9 - 2023 - Paper 1
Question 9
The graph of a cubic function, y = f(x), is given below.
Which of the following functions has an inverse relation whose graph has more than 3 points with an x-coord... show full transcript
Worked Solution & Example Answer:The graph of a cubic function, y = f(x), is given below - HSC - SSCE Mathematics Extension 1 - Question 9 - 2023 - Paper 1
Step 1
A. y = √f(x)
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Answer
The square root function can only provide one output for each input, hence it will not create multiple points with the same x-coordinate.
Step 2
B. y = 1/f(x)
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Answer
This function could lead to issues if f(x) equals zero, causing undefined behavior at those points and will not guarantee more than three points with the same x-coordinate.
Step 3
C. y = f(|x|)
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Answer
This function creates a symmetry about the y-axis. As a result, it would not typically lead to more than three distinct outputs for a single input.
Step 4
D. y = |f(x)|
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Answer
The absolute value function modifies all negative outputs of f(x) to positive, resulting in multiple outputs for certain input values. Therefore, this option will have more than three points with x-coordinate of 1.
