Both the general shape of a polynomial and its end behavior are heavily influenced by the term with the largest exponent. The most complex behavior will be near the origin, as all terms impact this behavior, but as the graph extends farther into positive and/or negative infinity, the behavior is almost totally defined by the first term. When sketching the general shape of a function, the most accurate method (if you cannot use a calculator) is to solve for some representative points (find y at x= 0, 1, 2, 5, 10, 20). If you connect the points with a smooth curve, you can make projections about where the graph is headed at either end.
End behavior is given by:
1. x^4. Terms with even exponents have endpoints at positive y ∞ for positive and negative x infinity.
2. -2x^2. The negative sign simply reflects x^2 over the x-axis, so the end behavior extends to negative y ∞ for positive and negative x ∞. The scalar, 2, does not impact this.
3. -x^5. Terms with odd exponents have endpoints in opposite directions, i.e. positive y ∞ for positive x ∞ and negative y ∞ for negative x ∞. Because of the negative sign, this specific graph is flipped over the x-axis and results in flipped directions for endpoints.
4. -x^2. Again, this would originally have both endpoints at positive y ∞ for positive and negative x ∞, but because of the negative sign, it is flipped to point towards negative y ∞.
12 x 40 = hours she worked = 480
3 x 31 = appointment fee = 93
480 + 93 = 573
The <em>correct answer</em> is:
A) There is a vertical shift of n units.
Explanation:
When a parent function is transformed, each type of transformation results ina different change in the graph.
The parent function in this question is f(x) = sin(x).
Adding n units to the end of this function would result in f(x) = sin(x) + n.
When a function is transformed by adding a constant to the end of a function results in a vertical shift by that number of units. In this case, it would be a vertical shift n units.
Willow = 63in
Jayder = 6ft 5in
1 foot equals 12 inches
6x12=72
So 72 inches plus 5 inches equals 77
So now you subtract Willows height from Jaydens height
77 - 63 = 14
Jayden is 14 inches taller
