Question

**1. **A model airplane will be an exact copy of the original, but at the size. The original

airplane is 230 feet long. How many feet long should the model be?

**Step 1:** Write a proportion that represents the problem. Let *x* = length (in feet) of the model airplane. **(2 points)**

**Step 2:** Solve the equation you wrote in Step 1 for *x*. Show your work. **(2 points)**

**Step 3:** How many feet long should the model be? **(1 point)**

**RATIONAL EXPRESSIONS**

**2. **Determine what values make this rational expression undefined:

** Hint:** A rational expression is undefined when its denominator is 0.

**Step 1:** Make the denominator of the expression equal to 0. **(0.5 points)**

**Step 2:** Solve the equation from Step 1 by factoring. Show your work. **(4 points)**

**Step 3:** What values of *x* make the expression undefined? **(0.5 points)**

**3. **Write in simplest terms. Show your work. **(3 points)**

**SIMPLIFYING EXPRESSIONS**

**4. **Use the hints to simplify each rational expression. Show your work and reduce all answers to simplest form. **(12 points; 3 points each)**

**A. Hint:** Find the common denominator and then add.

**B. Hint:** Find the common denominator and then subtract.

**C. Hint:** Multiply the first fraction by the reciprocal of the second fraction. Factor the expressions.

**D. Hint:** Factor the trinomial and then multiply the fractions together.

**DIRECT AND INVERSE VARIATIONS**

**5. **Determine if each set of points represents a direct or inverse variation.

**REMEMBER:**

Direct variation can be written *y* = constant(*x*).

Inverse variation can be written .

**A. **(2, 10), (7, 35), (12, 60)

**Step 1:** As *x* increases, does *y* increase or decrease? **(1 point)**

**Step 2:** What is the constant of variation? **(1 point)**

**Step 3:** Is this an example of direct variation or inverse variation? Explain your answer. **(2 points)**

**B. **(0.8, 4), (1.6, 2), (5, 0.64)

**Step 1:** As *x* increases, does *y* increase or decrease? **(1 point)**

**Step 2:** What is the constant of variation? **(1 point)**

**Step 3:** Is this an example of direct variation or inverse variation? Explain your answer. **(2 points)**

**C. **(1.5, 4), (2, 3), (12, 0.5)

**Step 1:** As *x* increases, does *y* increase or decrease? **(1 point)**

**Step 2:** What is the constant of variation? **(1 point)**

**Step 3:** Is this an example of direct variation or inverse variation? Explain your answer. **(2 points)**

**6.** Graph the rational function .

**Step 1:** Find all of the function's zeros and vertical asymptotes. Plot and label them on the number line. **(3 points)**

**Step 2:** Create a sign chart. Each test number in the table below falls before or after a zero or vertical asymptote in the function G(*x*). Use this information to transform your answer to Step 1 into a sign chart. **(4 points)**

*xG*(*x*)Positive or negative−70.75Positive−1.5−0.78Negative01.33Positive2.5−1.29Negative51.75Positive

**Step 3:** The function *G*(*x*) has a horizontal asymptote at *y* = 1. Use this information along with your answers from Steps 1 and 2 to sketch a graph of *G*(*x*). **(6 points)**

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