Let's match the descriptions with the graphs based on the provided functions:

1. $y = x^2$

   • This is a U-shaped parabola, decreasing for $x < 0$ and increasing for $x > 0$.
   • Description: c. decreasing function, 0, increasing function.

2. $y = x^3$

   • This is a cubic function, always increasing for all $x$.
   • Description: b. always increasing function.

3. $y = e^{-x}$

   • This is an exponential decay function, always decreasing as $x$ increases.
   • Description: a. always decreasing function.

4. $y = e^x$

   • This is an exponential growth function, always increasing as $x$ increases.
   • Description: d. increasing function, 0, increasing function.

Final match:

• $y = x^2$: c
• $y = x^3$: b
• $y = e^{-x}$: a
• $y = e^x$: d

Would you like further explanation on any of these functions or their graphs?

Here are 5 related questions:

1. What is the general shape of polynomial functions?
2. How does the derivative of $y = e^x$ relate to its behavior?
3. What are the key differences between $y = x^2$ and $y = x^3$ regarding their graphs?
4. What are real-life applications of the exponential decay function $y = e^{-x}$?
5. Can you find the turning points of $y = x^2$ and describe their significance?

Tip: Exponential functions $y = e^x$ and $y = e^{-x}$ are widely used in modeling growth and decay, such as in population dynamics or radioactive decay.