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 ∞.
Answer:
your answer should be 4095
Answer:
The Volume for r is 30 square units
Step-by-step explanation:
You break apart the two shapes the smaller shape is 12 square units and the bigger shape is 18 square units you add them together and BOOM 30 square units
Answer:
Step-by-step explanation:
we know that
The dimensions of the rectangular backyard in the actual are 300 feet by 600 feet
The dimensions of the rectangular backyard in the blueprint are 30 units by 60 units
therefore
If the radius of the circular flower garden in the actual is 60 feet
then
the radius of the circular flower garden in the blueprint is 6 units
Find the center of the radius in the blueprint
Remember that the circular flower garden is in the center o the backyard
so
To find out the center, determine the midpoint of the rectangular backyard
C((0+30)/2,(0+60)/2)
C(15,30)
The equation of a circle in center radius form is equal to
where
(h,k) is the center
r is the radius
we have
substitute
