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
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
