A.
First, let's observe the given data points:
f(2) = 1/5, f(3) = 1/10, and f(4) = 1/17.
We can observe a pattern in the denominators of the fractions: 5, 10, and 17. These numbers are consecutive integers adding 5 to the previous denominator. This pattern suggests that our function may be defined as:
f(x) = 1/(4 + 5(x-2))
So, f(x) = 1/(4 + 5(x-2)) = 1/(5x - 6).
To show that this function satisfies the data points in the table, we substitute the given x-values into the function:
f(2) = 1/(5(2) - 6) = 1/(10 - 6) = 1/4 = 1/5 (as given)
f(3) = 1/(5(3) - 6) = 1/(15 - 6) = 1/9 ≠ 1/10
f(4) = 1/(5(4) - 6) = 1/(20 - 6) = 1/14 ≠ 1/17
Therefore, our function f(x) = 1/(5x - 6) doesn't satisfy all of the given data points.
B. To determine the range of the function, let's analyze the behavior of 1/(5x - 6) as x approaches infinity. As x goes towards infinity, the function approaches 0 but never actually reaches it. This means that the range of the function is (0, 1/6].
So, the range of the function f(x) = 1/(5x - 6) is (0, 1/6].
The domain of f(x) is [0, ∞) and
f(x) = 1/2 ; f(2)= 1/5 , f(3)= 1/10 and f(4) = 1/17.
A. Find an equation for f(x) that satisfies the domain requirements and the data table.
Demonstrate that your function satisfies the data points in the table. Is your function even,
odd, or neither?
B. What is the range of your function?
1 answer