In a sequence described by a function, what does the notation f(3) = 1 mean?
1 answer:
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Answer:
Option C (f(x) = )
Step-by-step explanation:
In this question, the first step is to write the general form of the quadratic equation, which is f(x) = , where a, b, and c are the arbitrary constants. There are certain characteristics of the values of a, b, and c which determine the nature of the function. If a is a positive coefficient (i.e. if a>0), then the quadratic function is a minimizing function. On the other hand, a is negative (i.e. if a<0), then the quadratic function is a maximizing function. Since the latter condition is required, therefore, the first option (f(x) =
) and the last option (f(x) =
) are incorrect. The features of the values of b are irrelevant in this question, so that will not be discussed here. The value of c is actually the y-intercept of the quadratic equation. Since the y-intercept is 4, the correct choice for this question will be Option C (f(x) =
). In short, Option C fulfills both the criteria of the function which has a maximum and a y-intercept of 4!!!
Answer:
(- 4, - 12 ) , (4, 12 )
Step-by-step explanation:
Given the 2 equations
y = 3x → (1)
y = x² + 3x - 16 → (2)
Substitute y = x² + 3x - 16 into (1)
x² + 3x - 16 = 3x ( subtract 3x from both sides )
x² - 16 = 0 ( add 16 to both sides )
x² = 16 ( take the square root of both sides )
x = ± = ± 4
Substitute these values into (1) for corresponding values of y
x = - 4 : y = 3 × - 4 = - 12 ⇒ (- 4, - 12 )
x = 4 : y = 3 × 4 = 12 ⇒ (4, 12 )
2 times what = -4?
-2 does
-2 x 2 = -4
-4 time what = 8?
Again, -2.
-2 x -4 = 8
You could do this over and over again or make a table, or you can make a function.
f(n) = f(1) • r
f(1) in this case is 2.
f(n) = 2 • r
r is rate of change, which is -2.
f(n) = 2 • -2
To find the 12th number in the sequence, just substitute n for 12.
f(12) = 2 • -2
f(12) = 2 • -2
-2^11 = -2048
2 x -2048 = -4096
So the 12th number in the sequence will be -4096.
-2 does
-2 x 2 = -4
-4 time what = 8?
Again, -2.
-2 x -4 = 8
You could do this over and over again or make a table, or you can make a function.
f(n) = f(1) • r
f(1) in this case is 2.
f(n) = 2 • r
r is rate of change, which is -2.
f(n) = 2 • -2
To find the 12th number in the sequence, just substitute n for 12.
f(12) = 2 • -2
f(12) = 2 • -2
-2^11 = -2048
2 x -2048 = -4096
So the 12th number in the sequence will be -4096.