# Exponential and Radical Expressions Problem Set

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.

a) Show work in this space.

b) Answer:

Show work in this space.

c) Answer:

Show work in this space.

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

Answer:

Explain your answer in this space.

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

Answer:

X

Y

Show work in this space.

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.

Answer:

Show work in this space

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?

Answer:

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.

Answer:

Show work in this space

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.

Answer:

Show work in this space.

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.

Answer:

Show work in this space.

#### Solution Preview

Please see the detailed solution with graphs in the attached files.

Explain an advantage of rational exponents over the radical sign:

The advantage would be that if the number has a radical sign, you would ...

#### 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.