Match the description with the graph.

- a b c d

y = x2

a. always decreasing function

- a b c d

y = x3

b. always increasing function

- a b c d

y = e-x

c. decreasing function, 0, increasing function

- a b c d

y = ex

d. increasing function, 0, increasing function

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?

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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.

Match the description with the graph. - a b c d y = x^2 a. always decreasing function - a b c d y = x^3 b. always increasing function - a b c d y = e^-x c. decreasing function, 0, increasing function - a b c d y = e^x d. increasing function, 0, increasing function

Learn how to match function descriptions with their respective graphs. This problem involves quadratic, cubic, and exponential functions, exploring their behavior. Suitable for students in Grades 9-12, covering key mathematical concepts like exponential growth and decay.

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