Im going over my pre calculus 12 exam, and I need help with one question from the chapter Transformations of graphs and stuff.

Combining Transformations

2y = f(5x-10)+8

The original points are (4,6) and the new points I got by translating it and stuff are : (14/5,20) But in the answer it says (29/5, 7)I have no idea how to get that :| Since there is 2y on the left side, I would divide by 2 to get rid of it, and I would do the same on the other side, which would give me..

y = 1/2f(5(x-2))+8

To solve this problem, let's break it down step by step:

1. Start with the equation: 2y = f(5x - 10) + 8
2. Divide both sides of the equation by 2 to simplify it: y = (1/2)f(5x - 10) + 4
3. Now we have a transformed function of f(5x - 10) with an additional transformation of (1/2) vertically and +4 vertically.
4. To find the new points after these transformations, we can substitute the x-values from the original points (4,6) into the transformed equation and solve for y.
- For the x-value of 4, substitute it into the equation: y = (1/2)f(5(4) - 10) + 4
- Simplify the expression inside the function: y = (1/2)f(10) + 4
- As you mentioned, the original points (4,6) and the new points you got were (14/5,20). However, let's double-check the calculations.
5. Compute the expression inside the function: f(10)
6. Substitute this value back into the equation: y = (1/2)(f(10)) + 4
7. Finally, substitute the known value of y for the new point (14/5,20) to solve for f(10):
20 = (1/2)(f(10)) + 4
Subtract 4 from both sides: 16 = (1/2)(f(10))
Multiply both sides by 2: 32 = f(10)
8. Therefore, f(10) = 32.

So, the coordinates of the new point after all the transformations are applied are (10,32). It seems there was a mistake in the calculation you provided, and the correct answer is (10,32) instead of (14/5,20). Please double-check your calculations or consult your textbook/materials to ensure accuracy.