Even and odd functions are similar in the fact that they are both functions. However they are also different. Even functions are reflective over an axis, odd functions are not. A function is odd if the highest exponent is odd: y=2x^5+3x^2-x+2. A function is even if the highest exponent is even: y=x^2+2x-5. Every even function must have the characteristic that for every negative x value, f(-x)=f(x). A function can only be even if this statement is true. Every odd function must have the characteristic that for every negative x value, f(-x)=-f(x). Just as for even, a function can only be odd if this statement is true.
Factors and zeros are essentially the same thing. For example, if a factor form of an equation is (x-2)(x-1)(x+5), the zeros are x=2,1,-5. Division can help us factor polynomials because it gives us the zeros. The zeros can then be put into factors. The highest degree of the polynomial tells us how many zeros there will be. For example, if the equation is 3x^3+x^2+2x-5 then there will be three zeros.
Desmos Art 1: This graph looks like this because there are 2 different kinds of equations. The first is a form of x^2+y^2=(some number). This equation forms the circles in the center. The bigger the "some number" gets, the larger the radius of the circle. The other equation is a form of y=(some number)abs((cosx)/x). The larger the "some number" gets, the farther away the points get. The red and blue parts are more distant than the inner black parts. The two colors overlapping give it a 3D effect.
Desmos Art 2: This graph looks as it does because it uses many variations of the sin function. We can change the position of of the graph by adding a y intercept. I did that at 5, -5, 10, -10. When you add a - before the sign it flips the x intercepts so the lane waves the opposite way.
Desmos Art 3: This final graph looks this way because of the tangent function. Although it looks complex, it's really just 4 equations. The tangent function crosses the x-axis at one spot. Changing the number before the x will change the width of the graph. Putting a number before the tangent symbol flips the graph the other way from left to right, to right to left.
Stafford subsidized loans are available only to undergraduate students, and are based on financial need (as determined by the FAFSA). Students must be enrolled at least half-time in order to qualify for this loan. The interest rate is 4.66% and is subsidized while the borrower is in school.
Stafford Unsubsidized loans are available to both graduate and undergraduate students who are enrolled at least half-time. These loans are not need-based and no payments are required while the student is in school. There is a 4.66% interest rate for undergraduate students and a 6.21% interest rate for graduate students.
A Perkins loan is a need-based federal loan available to graduate and undergraduate students. Students applying for this loan must be enrolled at least half-time. There is no loan fee for a Perkins loan, and there is a 5% fixed interest rate. Undergraduate students can receive up to $5,500 a year, totaling no more than $27,500, while graduate students can receive up to $8,000 a year, totaling a maximum of $60,000.
If I attend Grand Valley State University next year, I will pay $14,960 per year.
$14,960 per year @ 6.31%