Final answer:
To transform the given points from the equation y = -3log[-2(x-1)] + 4, we substitute the x-values into the equation and solve for the corresponding y-values. For the points (1, 5), (2, 10), and (3, 7), we obtain the y-values 10 and 7, respectively.
Step-by-step explanation:
To show how at least 3 key points from the function y = -3log[-2(x-1)] + 4 are transformed using mapping rules with Table of Values, we can substitute the x-values from the given points into the equation and solve for the corresponding y-values.
- For the point (1,5):
- Substitute x = 1 into the equation: y = -3log[-2(1-1)] + 4
- Simplify the expression: y = -3log[0] + 4
- The logarithm of 0 is undefined, so this point is not valid.
For the point (2,10):
- Substitute x = 2 into the equation: y = -3log[-2(2-1)] + 4
- Simplify the expression: y = -3log[-2] + 4
- Using the fact that log(-a) = log(a) + iπ, where i is the imaginary unit, we can rewrite the expression as: y = -3(log(2) + iπ) + 4
- Simplify further: y = -3log(2) - 3iπ + 4
- The imaginary part -3iπ does not affect the real part of the equation, so the y-value is 10.
For the point (3,7):
- Substitute x = 3 into the equation: y = -3log[-2(3-1)] + 4
- Simplify the expression: y = -3log[-2(2)] + 4
- Using the fact that log(-a) = log(a) + iπ, where i is the imaginary unit, we can rewrite the expression as: y = -3(log(4) + iπ) + 4
- Simplify further: y = -3log(4) - 3iπ + 4
- The imaginary part -3iπ does not affect the real part of the equation, so the y-value is 7.