The point (1,-2) is on the graph of f(x). Describe the following transformations on f(x), and determine the resulting point.

Question 5 options:

a)
g(x)=2f(x)+3

b)
g(x)=f(x+1)−3

c)
g(x)=−f(2x)

d)
g(x)=−f(−x−1)+3

To determine the resulting point for each transformation, we need to follow these steps:

1) Start with the given point (1, -2).

2) Apply the transformation described in each option to the given function, f(x).

a) g(x) = 2f(x) + 3
To find the resulting point, substitute x = 1 into the transformed function:
g(1) = 2f(1) + 3
The resulting point is g(1), so you need to find the value of f(1) using the original function, f(x).

b) g(x) = f(x + 1) - 3
Substitute x = 1 into the transformed function:
g(1) = f(1 + 1) - 3
Again, you need to find the value of f(2) using the original function.

c) g(x) = -f(2x)
Substitute x = 1 into the transformed function:
g(1) = -f(2 * 1)
Find f(2) using the original function.

d) g(x) = -f(-x - 1) + 3
Substitute x = 1 into the transformed function:
g(1) = -f(-1 - 1) + 3
Find f(-2) using the original function.

Once you find the values of f(x) or f(x + k) needed for each option, substitute them back into the corresponding transformed equation to calculate the resulting points.