Algebra Questions. See attached file for full problem description.
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.
Please provide sources used.
1) Solve the following equations.
2) Is an identity (true for all values of x)?
3) 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.
4) 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.
5) For the equation x - 2*sqrt(x) = 0 perform the following:
a) Solve for all values of x that satisfies the equation.
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?
7) Suppose you travel north for 65 kilometers then travel east 75 kilometers. How far are you from your starting point?
8) The volume of a cube is given by V = s^3, where s is the length of a side. Find the length of a side of a cube if the Volume is 1000 cm3.
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.