A. To find an equation for f(x) that satisfies the data table, we can start by noticing that the denominators of the given values follow a pattern: 2, 5, 10, 17. These numbers are actually the sequence of positive integers minus 1, so we can express f(x) as:
f(x) = 1/(x^2 - 1)
To demonstrate that this equation satisfies the data points in the table, we can plug in the given x values:
f(1) = 1/(1^2 - 1) = 1/0 (undefined)
f(2) = 1/(2^2 - 1) = 1/3
f(3) = 1/(3^2 - 1) = 1/8
f(4) = 1/(4^2 - 1) = 1/15
The function does not perfectly match the data points, however the general trend is followed. This function is neither even nor odd.
B. To find the range of the function f(x) = 1/(x^2 - 1), we need to consider the limits as x approaches the boundaries of the domain [0, ∞). As x approaches 0, f(x) approaches 1, and as x approaches infinity, f(x) approaches 0. Therefore, the range of the function is (0, 1].
The domain of f(x) is [0, ∞) and
f(1)= 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