Instructions: drag the tiles to the boxes to form correct pairs. not all tiles will be used. match each verbal description to its equivalent function rule as applied to the given function below.

We have the following function:
(x)  = 3x - 7
The function f translated 6 units up and 2 units rigth:
6 units up:
y  = 3x - 7 + 6
2 units rigth:
y  = 3(x-2) - 7 + 6
y  = 3x - 6 - 7 + 6
Finally:
g(x)  = 3x - 7

The function f reflected about the y-axis and translated 7 units left:
reflected about the y-axis:
y = 3(-x) - 7
y = -3x - 7
translated 7 units left:
y = -3(x+7) - 7
y = -3x - 21 - 7
y = -3x -28
Finally:
g(x) = -3x - 28

The function f stretched vertically by a factor of 2 and translated up by 5 units:
stretched vertically by a factor:
y = 6x - 14
translated up by 5 units: 
y = 6x - 14 + 5 
y = 6x - 9
Finally:
g(x) = 6x - 9

 The function f stretched vertically by a factor of 4 and translated up by 9 units:
stretched vertically by a factor of 4:
y = 12x - 28
translated up by 9 units: 
y = 12x - 28 + 9 
y = 12x - 19
Finally:
g(x) = 12x - 19

Given that our original function is:
f(x)=3x-7

To Match each verbal description to its equivalent function rule we shall proceed as follows:
The function is translated 6 units up and 2 units right. 
since f(x) cuts through point (0,-7) the translation will give us the points (2,-7) and (2,-1), since the new line is parallel to the old, the slope will be m=3, thus the equation will be:
y=3x+c
using point (2,-1)
-1=3(2)+c
-1-6=c
c=-7
thus our equation will be:
y=3x-7
thus our new equation is: g(x)=3x-7

b] The function f is reflected about the y-axis and translated 7 units left. when we reflect the function f o y -axis, the new function will be:
y=-3x-7
when we translate this 7 units to the left we shall have:
y=-3x(x+7)-7
thus the final equation is
g(x)=-3x-21-7
simplifying we obtain:
g(x)=-3x-28

c] When f is stretched vertically by a factor of 2 and translated up by 5 units we shall have the following:
when f is stretched, the new function will be:
y=2(3x-7)
y=6x-14
when the above function is translated up by 5 units we shall have:
y=6x-14+5
thus simplifying the above the function becomes
g(x)=6x-9

c] The factor f is stretched vertically by a factor of 4 and translated up by 9 units.
when f(x) is stretched by a factor of 4, the new function will be:
f(x)=4(3x-7)
f(x)=12x-28
when the function is translated up by 9 units, the new function will be:
f(x)=12x-28+9
simplifying the above we get:
g(x)=12x-19