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