Question

Find the range of f(x) = 4x + 6 for the domain {-1, 2, 3, 4}.

Answer 1

Answer: range is {2, 14, 18, 22}

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Step-by-step explanation:

The domain is the set of all allowed x values.

Plug in x = -1 to find that...

f(x) = 4x+6

f(-1) = 4(-1)+6

f(-1) = -4+6

f(-1) = 2

The input x = -1 leads to the output y = 2.

In other words, the item -1 in the domain corresponds to the item 2 in the range.

Following similar steps, you should have the following:

• x = 2 leads to y = 14
• x = 3 leads to y = 18
• x = 4 leads to y = 22

Note: Each time x increases by 1, y increases by 4. This is directly tied to the slope of 4.

Therefore, we have this table of values.

`\begin{array}c\cline{1-2}\text{x} & \text{f(x)}\\ \cline{1-2}-1 & 2\\ \cline{1-2}2 & 14\\ \cline{1-2}3 & 18\\ \cline{1-2}4 & 22\\ \cline{1-2}\end{array}`

The domain {-1,2,3,4} leads to the range {2, 14, 18, 22}

Often with sets, order doesn't matter; however, in this case the order is fairly important to help see how the values pair up between the domain and range (eg: 3 pairs with 18).