Question

Martina creates the graph of function g by applying a transformation to function f.

Answer 1

Answer:

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.

Answer 2

Answer:

B.a vertical shift of 9 units up

Step-by-step 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.