Subjects functions

Domain Range

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Domain Range


1. The problem asks which figure represents a function where the range is not equal to the domain. 2. Let's analyze each figure: (a) A straight line passing through the origin increasing in the first quadrant. This line likely has domain and range both as all real numbers or at least the same intervals, so domain = range. (b) A line decreasing from left to right crossing the y-axis at 1 with an open circle at (5,0) on the x-axis, meaning x=5 is not included. The domain excludes 5, but the range is continuous. So domain ≠ range because the domain excludes a point but the range does not. (c) A curve starting from the origin going upwards steeply, like exponential growth. The domain is all real numbers (or at least non-negative if starting at origin), but the range is positive real numbers only, so domain ≠ range. (d) A curve starting from the origin going downwards steeply to the left, like a negative exponential. Domain and range are likely different because the curve is only on one side. 3. Conclusion: - (a) domain = range - (b) domain ≠ range - (c) domain ≠ range - (d) domain ≠ range Therefore, figures (b), (c), and (d) represent functions where the range is not equal to the domain.