Question

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​

Answer 1

B.a vertical shift of 9 units up

Explanation:

Given
`f(x) = 4x-2\\g(x) = 4x+7`

`g (x) = f (x) + k`

It means shifting
`f (x)\ k` unit vertically.

Now, we will find the value of
`k` for the given function

`g(x) = 4x+7\\\\add\ 2\ and\ subtract\ 2\\\\g(x) = 4x+7+2-2\\g(x) = 4x-2+9\\\\We\ have\ f(x)=4x-2\\\So,\ g(x)=f(x)+9`

`k=9`

Hence, vertical shift of 9 units.

Answer 2

C. a horizontal shift of 9 units left

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.