Multiple Graphs

by

Rob Walsh

For my final assignment, I return to the start and recreate all of the practice work from assignment zero. I group these eleven mini assignments into sections: linear, quadratic, sine, and other.

__Linear functions:__

In this section, problems 1, 2, and 3 begin with a set of linear functions and look briefly at what happens when I systematically alter either their y-intercept or their slope.

__Quadratic functions:__

In this section, problems 4 and 5 start with a set of quadratic functions and look briefly at what happens when I systematically alter either the vertical or horizontal positioning of their parabolic graph.

__Sine functions:__

In this section, I look at problem 6 in two ways as well as problems 7 and 8 in conjunction with them. It is a look into the sums of powers of sine functions in several different ways:

6a. (sin x)^{2} + (sin y)^{2} = n

6b. (sin x)^{3} + (sin y)^{3} = n

7. (sin (x^{2}))^{2} + (sin (y^{2}))^{2} = n

8. (sin x)^{3} + (sin y)^{3} = A(sin x)(sin y)

__Other graphs:__

In this section, I lump problems 9, 10, and 11 in to my final set of investigations into analysis of multiple graphs. Problem 11 (strophoid) is further broken down as well.

9. 4(x^{2} + y^{2} - 5x)^{3} = 27(5)^{2}(x^{2} + y^{2})^{2}

11a. y^{2}(x + 5) = x^{2}(n - x)

11b. y^{2}(x + n) = x^{2}(5 - x)

11c. y^{2}(x + n) = x^{2}(n - x)

11d. y^{2}(sin x + 5) = x^{2}(5 - sin x)

11e. (sin y)^{2}(x + 5) = x^{2}(5 - x)