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Note: You do not need to type anything in here, please include your answer with your uploaded scratch paper. 

Find the Laplace Transform of the following periodic function, whose graph is given below: Note: You do not need to type anything in here, please include your answer with your uploaded scratch paper. 

Use the definition of the Laplace Transform to determine:   Note: You do not need to type anything in here, please include your answer with your uploaded scratch paper. 

Solve the following IVP using the Laplace Transform: Note: You do not need to type anything in here, please include your answer with your uploaded scratch paper. 

Simplify completely:  23-526+4{“version”:”1.1″,”math”:”23-526+4″}

Given this function: f(x)=x2-7x+6×2-6x{“version”:”1.1″,”math”:”f(x)=x2-7x+6×2-6x”} What value(s) of x would make this function undefined? What is f(-3){“version”:”1.1″,”math”:”f(-3)”}? 

For a different quadratic function, the following table was created to find ordered pair solutions to create the graph.  Does this table include the vertex?  Explain your answer.  Would this table be useful in creating the parabola graph?  Explain your answer. You can type in your explanation or you can write your explanation on paper–your choice. x f(x) -2 15 -1 8 0 3 1 0 2 -1

Given the function:  f(x)=3×2-7x+2{“version”:”1.1″,”math”:”f(x)=3×2-7x+2″} What are the coordinates of the vertex? Does the parabola open up or down?  Explain how you know. Find 4 other ordered pair solutions that could be used to plot points to create the graph of this function.  Show how you determined/calculated the ordered pair solutions.

Solve the equation: x2-9=7×2+x-10{“version”:”1.1″,”math”:”x2-9=7×2+x-10″}

a.  Give an example of a function whose domain is all real numbers. b.  Give an example of a function whose domain is all real numbers except 3 and -2. c.  Give an example of a function whose domain is all real numbers that are greater than, or equal to, 5.