Question

Compare the function with the parent function. Without graphing, what are the vertex, axis of symmetry, and transformation of the given function? y=|6x-2|-7
(1/3,7); x=1/3; translated to the right 1/3 unit and up 7 units

(1/3,7); x=1/3; translated to the left 1/3 unit and down 7 units

(1/3,-7); x=1/3; translated to the right 1/3 unit and down 7 units

(1/3,-7); x=1/3; translated to the left 1/3 unit and up 7 units

Answer 1

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