To graph the square root function y=13x−3−−−−√+2 , complete the table of data points for the function.(2 points) x y 3 4 7

Question

To graph the square root function  y=13x−3−−−−√+2  , complete the table of data points for the function.(2 points) x	y 3	 4	 7

GPT-4o mini · Answer

To complete the table of data points for the function \( y = \sqrt{13x - 3} + 2 \), we will evaluate the function for the provided values of \( x \).

\[ y = \sqrt{13x - 3} + 2 \]

When \( x = 3 \): \[ y = \sqrt{13(3) - 3} + 2 = \sqrt{39 - 3} + 2 = \sqrt{36} + 2 = 6 + 2 = 8 \]
When \( x = 4 \): \[ y = \sqrt{13(4) - 3} + 2 = \sqrt{52 - 3} + 2 = \sqrt{49} + 2 = 7 + 2 = 9 \]
When \( x = 7 \): \[ y = \sqrt{13(7) - 3} + 2 = \sqrt{91 - 3} + 2 = \sqrt{88} + 2 \approx 9.38 + 2 \approx 11.38 \]

| \( x \) | \( y \) | |---------|----------------| | 3 | 8 | | 4 | 9 | | 7 | 11.38 |

So the values for \( y \) corresponding to \( x = 3, 4, \text{ and } 7 \) are 8, 9, and approximately 11.38, respectively.