What is the image point of (-4,7) after a translation left 4 units and down 4 units?

I guess the parent function to be: y = |8x|.

To translate a function m units to the right, you must substitute x by x-m. You had y = |8x|. You substitute x by x-1/4, to get:

y = |8(x-1/4)| = |8x-2|

So, the function was translated to the  right 1/4 unit.

To translate a function vertically n units, you add (translate up) or subtract (translate down) m to the function. You had y = |8x-2|. You subtract 7 to get:

y = |8x-2|-7

Hence, the parent function was translated 7 units down.

The vertex is the point where the content of the absolute value changes its sign, that is, the where it equals zero:

8x-2 = 0 <=> x=1/4

The x coordinate of the vertex is therefore x=1/4. To calculate the y coordinate of the vertex, you must substitute the x coordinate in the equation of the function, to get:

x=1/4 => y = |8(1/4)-2| - 7 = -7

The vertex is, therefore, (1/4,-7).

Finally, the axis of symmetry is a vertical line through the vertex: x=1/4 (the equation of a vertical line is of the form x=a).

The correct answer is D).

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step-by-step explanation: