Question

Properties of function, quick check

Answer 1

Here are some properties of functions that you can use as a quick check:

1. Domain and Range: Check the domain and range of the function to ensure that all inputs are valid and that the function outputs the correct range of values.

2. Injectivity: Check if the function is injective (one-to-one) by ensuring that each output corresponds to only one input.

3. Surjectivity: Check if the function is surjective (onto) by ensuring that the function covers all possible output values.

4. Bijectivity: Check if the function is bijective by ensuring that it is both injective and surjective.

5. Continuity: Check if the function is continuous by ensuring that there are no jumps or discontinuities in the graph of the function.

6. Differentiability: Check if the function is differentiable by ensuring that it has a well-defined derivative at all points in its domain.

7. Monotonicity: Check if the function is monotonically increasing or decreasing by looking at the sign of the derivative.

8. Symmetry: Check if the function has any symmetry, such as being even (symmetric about the y-axis) or odd (symmetric about the origin).