The graph of [math: y] versus [math: x2] x^2 is shown. The rule connecting [math: y] and [math: x] is :

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The problem asks to determine the rule connecting y and x^2 from the given graph of y versus x^2.
First, observe the plotted point on the graph: (x^2, y) = (2, 40). This means when x^2 equals 2, y equals 40.
If y is a function of x^2, the relationship can be written in the form y = m*(x^2), where m is the slope of the line in the y versus x^2 plot.
To find m, compute m = y / (x^2) = 40 / 2 = 20. Therefore, the equation is y = 20*(x^2).
Now evaluate each option:
- Option A: y = 20x^2. This matches the derived relation y = 20*(x^2), so it is consistent with the graph data.
- Option B: y = 20x. This expresses a linear relationship in x rather than in x^2, which does not fit a plot of y versus x^2 and would not pass through the given point when x^2 = 2.
- Option C: y = 40x^2. This would require y to be 40 when x^2 = 1, contradicting the observed value y = 40 when x^2 = 2, so it overestimates the slope.
- Option D: y = 0.1x^2. This implies a much smaller slope (0.1) than what the graph indicates, making it incompatible with the point (2, 40).
Thus, the option that correctly describes the rule connecting y and x^2 is the one that yields y = 20*(x^2) based on the provided point on the graph.

MUF0141 Fund. Mathematics Unit 1 - Semester 2, 2025

The graph of [math: y] versus [math: x2] x^2 is shown. The rule connecting [math: y] and [math: x] is :

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