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exponential and radical expressions

Solve the following equations and show your work:
1) sqrt of x - 2 = 1
2) sqrt of x^3 = 27
3) 3 sqrt of x^2 = 9
4) Is (sqrt of x)^2 an identity (true for all nonnegative values of x)?

x -2 -1 0 1 2

y .111 .333 1 3 9

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 Type:




1) For the function, y = 1
x - 2

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

Show graph here.

2) For the equation x - 2 sqrt of x = 0 , perform the following:

a)Solve for all values of x that satisfies the equation.
b) Graph the functions y = x and (y = 2 sqrt of x) on the same graph (by plotting points if necessary). Show the points of intersection of these two graphs.

Points of intersection:

3) 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 6 feet and 8 feet.

4) Suppose you travel north for 65 kilometers then travel east 75 kilometers. How far are you from your starting point?

5) The volume of a cube is given by V = s3, where s is the length of a side. Find the length of a side of a cube if the Volume is 1000 cm3.

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2. It is not true for all ...

Solution Summary

The solution is comprised of detailed solution of the equations and graphs related to exponential and radical expression. Supplemented with graphs, math equations and step-by-step explanations, the solution set provides the student a clear prospective on exponential and radical expressions.