Martina creates the graph of function g by applying a transformation to function f.
f(x) = 4x-2
g(x) = 4x+7
which transformation did martina apply?

a. a vertical shift of 9 units down
b. a vertical shift of 9 units up
c. a horizontal shift of 9 units left
d. a horizontal shift of 9 units right

C. a horizontal shift of 9 units left

Step-by-step explanation:

Look at this helpful chart:

Vertical Translations

translation up k units: g(x) = f(x) + k, where k > 0

translation down k units: g(x) = f(x) – k, where k > 0

Horizontal Translations

translation left k units:  g(x) = f(x + k), where k > 0

translation right k units:  g(x) = f(x – k), where k > 0

The change happening in Martina's graph is therefore a horizontal translation to the left.

step-by-step explanation:

this woman was an important writer and propagandist during the american revolution. she was a member of the committee of correspondence (in fact the committee was formed in her home) and was an advisor to many of the revolutionary leaders, including george washington and john adams. who was this revolutionary woman?

3-4

step-by-step explanation:

the answer is 3-4 because both 45 and 60 has a multiple of 15.

45/3=15

60/4=15

therefore the odds against selecting a red is 4-3