Consider the graph of the function g shown below. The domain of g is [0, 10], and the graph of g is comprised of two line segments and a quarter circle.
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
Please answer questions 4-6. Thank you!
![Consider the graph of the function g shown below. The domain of g is [0, 10], and the
graph of g is comprised of two line segments and a quarter circle.
8
4
3
1
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4
6
7
8.
10
1. The function F is defined on [0, 10]. It is an antiderivative of g and satisfies F(7) = 0.
Sketch a graph of F.
2. Use your knowledge of area to compute F(4). Explain your reasoning.
3. Write a formula for F using an appropriate integral of g.
4. The function G is defined on [0, 10]. It is an antiderivative of g and satisfies G(0) = -2.
Sketch a graph of G.
5. Compute G(3) and G(10).
6. Compare and contrast the graphs of F and G.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe6874539-24dd-4fb8-b649-d4f18557889b%2Fd43e6797-4b63-4b8d-8ea6-09b5aae53515%2Fg2y07nn_processed.png&w=3840&q=75)
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