Question

Make an input-output table for the function. Use 1, 1.5, 3, 4.5, and 6 as the domain. $$ y=\frac{9}{x}+10 $$

Short answer

The input-output table for the function \(y=\frac{9}{x}+10\), using the domain values 1, 1.5, 3, 4.5, and 6 is as follows: x | y ----------- 1 | 19 1.5 | 16 3 | 13 4.5 | 12 6 | 11.5

Step-by-step solution

Understand the given function

In the provided function \(y=\frac{9}{x}+10\), 'x' is the independent variable that is part of the domain. 'y' is the dependent variable determined by the output of the function for each input.

Substitute the domain values into the function

Now, replace 'x' in the function with each domain value and calculate the corresponding 'y' values. This means to plug each value into the equation and simplify it to find the corresponding output. The calculations are as follows: For \(x = 1\), \(y = \frac{9}{1} + 10 = 19\) For \(x = 1.5\), \(y = \frac{9}{1.5} + 10 = 16\) For \(x = 3\), \(y = \frac{9}{3} + 10 = 13\) For \(x = 4.5\), \(y = \frac{9}{4.5} + 10 = 12\) For \(x = 6\), \(y = \frac{9}{6} + 10 = 11.5