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%
I think the basketball will go in because it will follow the slope of the graph. This is a quadratic function that models an equation which matches the arc of the basketball. Factors that play into the ball going into the hoop would be: gravity, wind, the snap of the thrower's wrist, etc.
-My predictions were very close for 21 inches and 14 inches, but not very close for the 7 inch ramp. My 7 inch graph was so different because I thought the skateboard would go further in the same amount of time, but it didn't. My initial reasoning for the shape of these graphs was that I thought the incline would be fast and the decline would be slightly slower.
-The zeroes of my graph represented the start and end points.
-The three graphs were different when talking about zeroes, maximums, and minimums. The maximums got lower with each graph, and the minimums got higher. The first zero was 0 for each one because that's where it started. The last zero was different for each one because each trial ended at a different point.
-The slope is highest for the 21 inch ramp because the ramp was tallest, and therefore gave the skateboard the most speed. The slope of the 14 inch ramp was slightly lower seems the ramp was also lower. The slope for the 7 inch ramp was the lowest of the three because the height was the lowest, giving the skateboard less speed. It's rising the fastest from 0-10/15 seconds and falling from 10/15-17/35 seconds.
Graph (A) would mean that he is raising the flag at a consistent speed, not speeding up or slowing down. Graph (B) would mean that he started out raising it fast, but then slowed down at the end, almost plateauing. Graph (C) would mean that he is constantly speeding up and slowing down, speeding up and slowing down, but at the same rate. Graph (D) would mean that he starts out slow, and then speeds up at the end. Graph (E) would mean that he starts slow, increases speed very quickly, and then slows down at the end. Graph (F) would (be nearly impossibly) mean the he raises the flag the height of the whole pole instantly.
I think that Graph (D) shows the most realistic situation because I think you would start out slow, then speed up when you get the hang of it.
I think that Graph (F) shows the most unrealistic situation because it is impossible to raise the flag instantly without any time passing.
In this piece of "art", there are a lot of things going on. There are 6 separate equations, as seen below, and each equations is technically 2 equations put together. For example, in the first equation the two parts are -6 =< y and y =< 6. The first half would form the line at -6 and then shade up, while the second half would form the line at 6 and shade down. The same happens with the second equation (-6 =< x =< 6), but instead it is formed horizontally. For the last four, the equations are also two smashed into one. Again, -x =< y and y =< x. The first draws a line at -1x and shades down, while the second draws a line at 1x and shades upwards forming a triangle. This is true for the other three quadrants. Put them all together and you get a picture that slightly resembles the British flag.