A5a
Practice - Functions
TRY TO ANSWER IN TWO AND A HALF MINUTES.
QUESTIONS
QUESTIONS
1. In what ways can functions be described?
2. If f(x) = x³ + 5x² , the value of f(-3) is what?
3. Construct a table with two columns, x and f(x). In the first column write -5, 0, 5, 10 and 15. If f(x) = 2x + 4, what are the five entries in the f(x) column of your table?
4. If f(m) = √(100 - 4(3 + m)), what is f(m) when m = 6?
5. What is the sixth term in the following sequence: -14, -8, -2, +4, ....
6. You sell one item for $5.00. You sell two items for $4.75 each. You sell three items for $4.50 each. You sell four items for $4.25 each. What function describes your pricing scheme?
ANSWERS
1. Four ways. Algebraically, as in f(x) = x + 2. Numerically, in the form of a table with two rows or columns, one of which shows f(x) and the other of which shows x. Graphically, in which f(x) is equal to the value on the y-axis. Verbally, such as "You walk at three miles per hour."
2. Substituting directly, you can see that (-3)³ + 5(-3)² = -27 + 45 = 18.
3. If x = -5, f(x) = -6. If x = 0, f(x) = 4. If x = 5, f(x) = 14. If x = 10, f(x) = 24. If x = 15, f(x) = 34.
4. You do not need to simplify the equation. Just plug m = 6 into it, so that f(m) = √(100 - 36) = 8.
5. Each item is the preceding item plus 6. But be careful here. The question asks for the sixth item, not the fifth. The fifth item in the series is +10 and the sixth item is +16.
6. The unit price drops $0.25 as each item is added, after the first. Let equal the number of items. Then f(n) = $5.00 - $0.25 (n-1). Check your function by substituting values of n to see if it works.
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