Question

On a coordinate plane, an curved line with a negative slope begins at (0, 0) and extends toward negative infinity.
Which is the equation of the function in the graph?

Answer 1

To describe a curved line with a negative slope that begins at (0, 0) and extends toward negative infinity, we can consider a class of functions that generally exhibit this behavior. One common type of function that fits this description is a decreasing function, such as a negative exponential function or a negative power function.

1. **Negative Exponential Function**: An example could be:
\[
f(x) = -e^{-x}
\]
This function starts at (0, 0) and decreases toward negative infinity as \( x \) increases.

2. **Negative Power Function**: Another example could be:
\[
f(x) = -x^2
\]
This function also starts at (0, 0) and decreases towards negative infinity as \( x \) moves away from zero.

3. **Logarithmic Functions**: A logarithmic function with a negative constant might also work, such as:
\[
f(x) = -\ln(x+1)
\]
This also curves down, starting at (0, 0) and continuing toward negative infinity as \( x \) increases.

Each of these equations describes a function that starts at (0,0) and has a negative slope, trending downwards toward negative infinity. If you are looking for a specific function family or type of function to match a certain graph, it's helpful to have more detail about the behavior or shape you expect.