Which could be the graph of f(x) = |x - h| + k if h and k are both positive? image for option 1 image for option 2 image for option 3 image for option 4

In general, if you have a parent function, f(x), the graph of a daughter function f(x - h) + k is related with the graph of the parent function as per these rules:

Therefore, the graph of  f(x) = |x - h| + k is a translaion of h units to the right and k units upward fo the function f(x) = |x|.

Since, the graph of f(x) = |x| has vertex (0,0), the graph of f(x) =  |x - h| + k has vertex (h, k).

To visualize the images of the graph, assume some positive value for h and k. For instance, h = 3 and k = 5.

See the image attached showing the graphs for the functions f(x) = |x| (red line) and f(x - 3) + 5 = |x - 3| + 5 (blue line). As you can see, the blue line is the translation of the red line 3 units to the right and 5 units upward.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

1.3 million hoops i believe