Question

Instructions:Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.

Answer 1

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

Answer 2

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