Question

Which ONE of the following curves represents the equation \( y = e^{-x} \)?
Figures not to scale

• A.

  

• B.

  

• C.

  

• D.

  

Hint:

Check the sign of the derivative of \( e^{-x} \) and see whether the curve should rise or fall as x increases.

Answer 1

The Correct Option is B

Since $y = e^{-x}$ can be rewritten as $y = \left(\dfrac{1}{e}\right)^x$, this is an exponential decay curve, and matching it to a picture just means checking growth direction and shape.

1. Option A: This curve starts near zero on the left, sits at $(0,1)$, and rises steeply on the right. That is growth as $x$ increases, which fits $y = e^{x}$, not $y = e^{-x}$.
2. Option B: This curve is steep and high on the left, comes down through $(0,1)$, and flattens toward the x-axis on the right. That is decay as $x$ increases, matching $y = e^{-x}$ exactly.
3. Option C: This is a V-shaped curve with a sharp corner at the origin, which looks like $y = |x|$ style behaviour, not a smooth exponential.
4. Option D: This is a U-shaped curve touching zero at the origin, which looks like a curve such as $y = x^2$, not an exponential that never reaches zero.

Only option B has the decaying exponential shape that $y = e^{-x}$ actually has, so option B is correct.