Math 536: Test #4 : Square Root Function Name: Date

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Math 536:
Test #4 : Square Root Function
Name: ________________________
(ref: test4.536.99)
Date: _________________________
Solve the following questions in the spaces provided. Show all work very clearly. A graphical
calculator may be used for assistance but the work to get the answer must be shown on this paper.
1. Simplify the following expressions:
a)
√ 6 − √3
−−−−−−
2√5
b)
3√27
−−−−
√18
2.
3. State the restrictions (conditions) and solve the equations algebraically:
a) √ x + 1 = 5
b) −2 √ (2x − 1) + 7 = 3
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4. From 1988 to 1998, a city’s population increased at a progressively slower rate according
to the rule P(x) = 1800 √(x + 2) + 22000, where x is the number of years since 1988 and
P(x), the city’s population. (note: this entire problem can be done on the graphing
calculator)
a) On a coordinate system, sketch the graph that represents this situation:
b) What was the city’s population in 1988?
c) What was the city’s population in 1998?
d) If the population continues to increase at the same rate, what year will the city’s
population reach 30 000?
5. Find the critical pairs of the function g(x) = 3√2(x−4) −1 using those belonging
to the basic function.
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6. Jessica has a greenhouse built adjacent to the exterior wall of her kitchen,
as shown in the sketch. The greenhouse roof resembles a semi−parabola of
equation y = (1/4) √(7 − 2x) + 2, where x is the distance in metres separating
the kitchen from the greenhouse’s far wall, and y is the height of the greenhouse in metres.
a) What is the length of the greenhouse?
b) What is the greenhouse’s maximum height to the nearest tenth of a metre?
7. Find all the properties of the function defined by f(x) = (−1/2) √(x + 7) + 1
(sketch graph)
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8. Use algebra to solve the following equation in IR:
2 √(2x + 1) = 3 √ x
9. Find the y−intercept of the following function:
h(x) = −2 √(2x + 3) + 2
10. Simplfy the radicand:
4 √ a3 − 2a2b + ab2
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