8. Explain the transformations of the graph y=23sqrtx+2-3 from its parent function y=x.
3 is in the middle of the square root symbol
The transformation of the graph y = 23√x + 2 - 3 from the parent function y = x involves three main transformations:
1. Vertical Translation: The "-3" outside the square root symbol represents a vertical translation of 3 units downward. This shifts the entire graph down by 3 units compared to the parent function y = x.
2. Horizontal Compression: The coefficient of 23 before the square root symbol represents a horizontal compression by a factor of 1/23. This means that the graph will be narrower compared to the parent function y = x.
3. Horizontal Translation: The "+2" inside the square root symbol represents a horizontal translation of 2 units to the left. This shifts the graph to the left compared to the parent function y = x.
Combining all these transformations, the graph of y = 23√x + 2 - 3 will be narrower, shifted to the left, and shifted downward compared to the parent function y = x.