Question

which of the following graphs represents a function that is both non - linear and decreasing? a graph that forms a straight line going downwards from left to right; a graph that forms a straight horizontal line; a graph that forms a curved line going downwards from left to right; a graph that forms a circle

Explanation:

1. Analyze Option A: A straight - line graph is a linear function. A straight line going downwards from left to right is a linear decreasing function, so it does not meet the non - linear requirement.
2. Analyze Option B: A horizontal straight line represents a constant function (linear, with a slope of 0). It is not decreasing (in the strict sense of a function that has a negative rate of change) and is linear, so it is not the answer.
3. Analyze Option C: A curved line is a non - linear graph. If it is going downwards from left to right, it means that as the input (x - value, moving from left to right) increases, the output (y - value) decreases. So this graph represents a non - linear and decreasing function.
4. Analyze Option D: A circle does not represent a function (by the vertical line test, a vertical line can intersect a circle at two points). So it cannot be the graph of a function.

Answer:

C. A graph that forms a curved line going downwards from left to right