Question

The graph of y=e^x is transformed as shown in the graph below. Which equation represents the transformed function?
y=e^x-3
y=e^x+3
y=e^x+3
y=e^x+3x
y=e^x-3+^+3

Answer 1

I don't see the graph. Could you either upload it or describe the transformation (horizontal/vertical shift, reflection, stretch)?

Meanwhile, here are quick ways to identify the correct equation from the graph:

- Check the horizontal asymptote. For y = e^x the asymptote is y = 0. A vertical shift by k gives asymptote y = k, so the transformed function will be y = e^{x-h} + k (h = horizontal shift, k = vertical shift).
- If the asymptote is y = 3 → y = e^{x-h} + 3 (often just y = e^x + 3 if there's no horizontal shift).
- If the asymptote is y = −3 → y = e^{x-h} − 3.

- Check the y-intercept (value at x = 0). If you know h and k, y(0) = e^{-h} + k. Use that to solve for h or confirm k.

- Reflections/stretch: a negative sign (y = −e^{x-h} + k) flips across the asymptote; a factor a (y = a e^{x-h} + k) changes steepness.

Note: the option y = e^x + 3x is not a standard exponential transformation (it's exponential plus a linear term), so it’s unlikely to be the intended transformation.

If you upload the graph or say where the horizontal asymptote and a couple of points are (for example the y-intercept and the x-value where y = k+1), I’ll pick the exact equation.