Given the function y = 3x + 4 and the domain 3 to 14, how can I determine the range of this function?

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To determine the range of the function y = 3x + 4 within the specified domain of 3 to 14, we need to evaluate the function at the endpoints of this domain.

The first step is to calculate the value of y when x = 3:

y = 3(3) + 4 = 9 + 4 = 13

Next, we will find the value of y when x = 14:

y = 3(14) + 4 = 42 + 4 = 46

Now, we can summarize our findings:

  • When x = 3, y = 13.
  • When x = 14, y = 46.

Since the function y = 3x + 4 is a linear equation, it continuously increases as x increases within this domain. Therefore, the range of the function will span from the minimum value of y (when x = 3) to the maximum value of y (when x = 14).

Thus, the range of the function when the domain is from 3 to 14 is:

Range: [13, 46]

In conclusion, for the function y = 3x + 4 with the given domain, the range is [13, 46].

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