## Precalculus Practice Exam

Part 3 Test 4 Time: 1 hour

• Write the expression

as one simplified " " term.

• Determine the domain that makes the original expression equivalent to the final expression.

Answer: x>6 or in interval notation, .

1. Solve the following equation for x:

• Solve the following equation for x:

• What is the common domain of the two functions?

Answer: The common domain of both functions is -5<x<10, or in interval notation, (-5,10).

2. A certain town in Texas, had a population of 400,000 in 1950, and a population of 300,000 in 1990.
• Derive the population equation.

Answer: , where t=0 corresponds to the year 1950.

• What was the population in 1980?

Answer: The population in 1980 was approximately 322,371 people.

3. Find the special parabola that contains the points (-1,-6), (2,-3), and (3,-14).

Answer: The formula for the parabola is

• Find the inverse of the function .

• Give the domain and range for f(x) and .

Answer: The domain of f(x) is all real numbers, or interval notation, .
The range of f(x) is y>0, or in interval notation, .

The domain of is x>0, or in interval notation, .
The range of is all real numbers, or in interval notation, .

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Sun Jun 22 21:33:16 MDT 1997