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The solutions to exam 3d for math 002, focusing on the square root function and rational exponents. It includes instructions, graph transformations, numerical expressions, and graph analysis. Students are required to show their work and provide exact answers.
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Square Root Function and Rational Exponents
Wednesday, November 12, 1997 NAME:_____ โโโโโโโโโโโDisc, time:_
INSTRUCTIONS: Please show all work in order to receive any partial credit. Unless otherwise specified, give exact answers in simplified form, i.e., do not use decimal approximations. BOX your final answers.
[19] 1. Use the function below to answer the following questions.
y = \Jx + 3 โ 4
[4] a. Describe the shifts of the basic square root function's graph that are necessary in order to obtain the graph of the function above.
Horizontal shift:_____โ โ ___ Vertical shift:_______.
[2] b. What is the starting point of the function above? Starting point:
[2] c. What is the yโ intercept, if any, of the function above? yโ
[4] d. What is(are) the :r-intercept(s), if any, of the function above?
[3] e. Graph the function in the space provided and LABEL all points that you found above
[2] f. What is the domain of the function above? Domain:______________
y โข> -y [2] g. What is the range of the function above? Range:โโโ'_________
[9] 2. Rewrite each numerical expression in radical form and then evaluate, if possible, without using a calculator.
[3] a. (-
ยฃ
)
2.
[12] 3. Simplify each of the following expressions, rationalizeStlfappropriate~aenominators, and write your final answer without negative exponents. Assume that x > 0 and y > 0.
= Z X V A
\TxT-3v ]
li
-3*
9 X
[10] 5. The velocity, v, in feet per second of a rolling ball as a function of time, t, in seconds, is given by
[2] a. What is the initial velocity of the ball? Initial velocity:.
[3] b. How long does it take the ball to come to rest? Time to rest:..
[3] c. At what time is the velocity of theHjall one-third of its original velocity?_
[2] d. How fast is the ball travelling at 6 seconds? Velocity at 6 sec:โ_______