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

6a. and 6a. combined

7. (sin (x²))² + (sin (y²))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(x² + y² - 5x)³ = 27(5)²(x² + y²)²

10. r = cos (5O) - ncos (O)

11a. y²(x + 5) = x²(n - x)

11b. y²(x + n) = x²(5 - x)

11c. y²(x + n) = x²(n - x)

11d. y²(sin x + 5) = x²(5 - sin x)

11e. (sin y)²(x + 5) = x²(5 - x)

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