# How do you find the range of the function y=2x^2+1 when the domain is {9, 3, 99}?

Jun 19, 2015

This function has a range between $19$ an $19603$

#### Explanation:

The domain of the function has only 3 elements, so it will be easy just to calculate the values:

$f \left(3\right) = 2 \cdot {3}^{2} + 1 = 2 \cdot 9 + 1 = 18 + 1 = 19$
$f \left(9\right) = 2 \cdot {9}^{2} + 1 = 2 \cdot 81 + 1 = 162 + 1 = 163$
$f \left(99\right) = 2 \cdot {99}^{2} + 1 = 2 \cdot 9801 + 1 = 19602 + 1 = 19603$

So the function has only the values from range: <19;19603>

Jun 19, 2015

For a function with finite domain, evaluate the function at each value. The set of results is the range.

#### Explanation:

The range of a function is the set of all values the function attains (the set of 'y-values' or of 'outputs')

For the function given, we find:
$f \left(9\right) = 163$
$f \left(3\right) = 19$
$f \left(99\right) = 19 603$
So the range is $\left\{163 , 19 , 19603\right\}$,