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# Exponential and Radical Expressions Problem Set

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While the radical symbol is widely used, converting to rational exponents has advantages. Explain an advantage of rational exponents over the radical sign. Include in your answer an example of an equation easier to solve as a rational exponent rather then a radical sign.

1) Solve the following equations.
a) Show work in this space.

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2) Is an identity (true for all values of x)?

3) x -2 -1 0 1 2
y .25 .5 1 2 4

Given the table above, graph the function, identify the graph of the function (line, parabola, hyperbola, or exponential), explain your choice, and give the domain and range as shown in the graph, and also the domain and range of the entire function.

Graph
Graph Type
Explanation
Domain
Range

4) For the function, y = 1/(x -1)

a) Give the y values for x = -2, -1, 0, 1, 2, 3
X
Y
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b) Using these points, draw a curve.
Show graph here.

5) For the equation, perform the following:
a) Solve for all values of x that satisfies the equation.
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b) Graph the functions on the same graph (by plotting points if necessary). Show the points of intersection of these two graphs.

c) How does the graph relate to part a?

6) A right triangle is a triangle with one angle measuring 90°. In a right triangle, the sides are related by Pythagorean Theorem, where c is the hypotenuse (the side opposite the 90° angle). Find the hypotenuse when the other 2 sides' measurements are 3 feet and 4 feet.
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7) Suppose you travel north for 35 kilometers then travel east 65 kilometers. How far are you from your starting point? North and east can be considered the directions of the y- and x-axis respectively.

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8) The volume of a cube is given by V = s^3. Find the length of a side of a cube if the Volume is 729 cm3.
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