Question

Which quadrants and axes does `f(x)=-xe^x` pass through?

Answer 1

`f(x)` runs through Q2 and Q4, intersecting both axes at `(0, 0)`.

Explanation:

Given:

`f(x) = -xe^x`

Note that:

• `e^x > 0" "` for all real values of `x`
• Multiplying `y` by any positive value does not change the quadrant in which `(x, y)` lies, or any axis on which it lies.

So the quadrant/axes behaviour of `f(x) = -xe^x` is the same as that of `y = -x`.

Note that `y = -x` means that `x` and `y` are of opposite signs, except at `(0, 0)`.

So `f(x)` runs through Q2 and Q4, intersecting both axes at `(0, 0)`.

graph{-xe^x [-10, 10, -5, 5]}