Answer: (1/3,-7); x=1/3; translated to the right 1/3 unit and down 7 units
Step-by-step explanation:
The parent function is:
g(x) = IxI
And we have:
f(x) = I6x - 2I - 7
We canr rewrite f to get:
f(x) = 6*Ix - 1/3I - 7
Then, now let's define some transformations:
If we start with g(x), a translation of N units to the right is:
f(x) = g(x - N)
if we start with g(x), a translation of N units up is:
f(x) = g(x) + N
A translation down would be:
f(x) = g(x) - N
And a vertical dilation of scale factor A is written as:
f(x) = A*g(x)
Then in this case we have:
A translation to the right of 1/3 units.
A dilation of scale factor 6.
A translation down of 7 units.
And the axis of symmetry will be when the absolute value part is equal to zero, or when
6*Ix - 1/3I = 0
And that is when x = 1/3.
Then the correct option is:
(1/3,-7); x=1/3; translated to the right 1/3 unit and down 7 units
