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1) Solve the following equations algebraically. You must show all your work. Learn how to type math roots and fractions by clicking on the link in the assignment list. Alternately, you may type [pic] as cuberoot(x) and show raising to the nth power as ^n, like x 3 is typed x^3.

a) [pic]

Answer: t = 8

Show your work here: T to the power of (2/3)* (3/2) = 4 to the power of (3/2) = 2 to the power of 2 * (3/2) = 2 to the power of 3 = 8

b) [pic]

Answer: x = 32

Show your work here: The power of 5 square of x = 3 – 1 = 2 so x = 2 to the power of 5 = 32

c) [pic]

Answer: x= 5/ 11

Show your work here: 3(x - 1) *2/3 =2*3*(x - 1) - 3(x - 1) (5x - 3)/(x - 1) 2(x-1) = 6(x - 1) - 3(5x - 3) 2x -2 =6x - 6 - 15x + 9 11x =2 - 6 + 9 =5 x=5/ 11

2) Solve algebraically and check your potential solutions:

a) [pic]

Answer: x = 2

Show your work here:

[pic]

[pic] X = 2: square root of 2 +2 then subtract 2 = 0 this answer works X = -1: square root of -1 + 2 then subtract (-1) = 0 this answer doesn’t work So x = 2

b)

[pic]

Show your work here: 4(x - 2) – x =-2 then 4x – 8 – x = -2 so 3x = 6 then x=2

What potential solution did you obtain? Explain why this is this not a solution. x=2: This is not a solution since it makes a denominator in the original equation equal to 0.

3) 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(round the answer to three decimal places) if the volume is

a) 800 cm3.

Answer: 9.283 cm

Show your work here: 800 = s to

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...MTH133 Unit 4– Individual Project – D 1. Graphing Transformations a) Given the function f(x) = x2 complete the following table. Must show all work for full credit. Answer: x f(x) -2 4 -1 1 0 0 1 1 2 4 Show your work here: For x = -2, f(x) = (-2)2 = 4 For x = -1, f(x) = (-1)2 = 1 For x = 0, f(x) = (0)2 = 0 For x = 1, f(x) = (1)2 = 1 For x = 2, f(x) = (2)2 = 4 b) Using the table from part a, graph the function f(x) = x2. For a tutorial on creating graphs in Excel and inserting graphs of functions please see the Assignment List. Answer: c) Given the function f(x) = x2 - 4 complete the following table. Must show all work for full credit. Answer: x f(x) -2 0 -1 -3 0 -4 1 -3 2 0 Show Work: For x = -2, f(x) = (-2)2 – 4 = 4 – 4 = 0 For x = -1, f(x) = (-1)2 – 4 = 1 – 4 = 0-3 For x = 0, f(x) = (0)2 – 4 = 0 – 4 = -4 For x = 1, f(x) = (1)2 – 4 = 1 – 4 = -3 For x = 2, f(x) = (2)2 – 4 = 4 – 4 = 0 d) Using the table from part c, graph the function f(x) = x2 - 4. For a tutorial on creating graphs in Excel and inserting graphs of functions please see the Assignment List. Answer: e) Given the graph of y=f(x) describe in words the transformation of y=f(x)-4. Answer: The graph of y=f(x)-4 is a 4 unit shift of the graph y = f(x) towards down. 2) Find the domain of the function and express the answer in interval notation. Explain in words or show the calculations for full credit. a) f(x) = 10x + 1 Answer: domain is (-∞, ∞) ...

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