The point (-12, 4) is on the graph of y = f(x). Find the corresponding point on the graph of y = g(x)? (Refer to below)

1) #g(x) = 1/2f(x)#
2) #g(x) = f(x-2)#
3) #g(x) = f(-x)#
4) #g(x) = f(4x)#
5) #g(x) = 4f(x)#
6) #g(x) = -f(x)#

I know the answers for 1, 3, and 5 are (-12, 2), (12, 4), and (-12, 16) respectively, but I don't know how to solve them.

1 Answer
Oct 13, 2017

Answer:

  1. #(-12,2)#
  2. #(-10,4)#
  3. #(12,4)#
  4. #(-3,4)#
  5. #(-12,16)#
  6. #(-12, -4)#

Explanation:

1:

Dividing the function by 2 divides all the y-values by 2 as well. So to get the new point, we will take the y-value (#4#) and divide it by 2 to get #2#.

Therefore, the new point is #(-12,2)#

2:

Subtracting 2 from the input of the function makes all of the x-values increase by 2 (in order to compensate for the subtraction). We will need to add 2 to the x-value (#-12#) to get #-10#.

Therefore, the new point is #(-10, 4)#

3:

Making the input of the function negative will multiply every x-value by #-1#. To get the new point, we will take the x-value (#-12#) and multiply it by #-1# to get #12#.

Therefore, the new point is #(12,4)#

4:

Multiplying the input of the function by 4 makes all of the x-values be divided by 4 (in order to compensate for the multiplication). We will need to divide the x-value (#-12#) by #4# to get #-3#.

Therefore, the new point is #(-3,4)#

5:

Multiplying the whole function by #4# increases all y-values by a factor of #4#, so the new y-value will be #4# times the original value (#4#), or #16#.

Therefore, the new point is #(-12, 16)#

6:

Multiplying the whole function by #-1# also multiplies every y-value by #-1#, so the new y-value will be #-1# times the original value (#4#), or #-4#.

Therefore, the new point is #(-12, -4)#

Final Answer