What type of transformation takes the graph of f(x)=|x| to the graph of g(x)=−3+|x|?

vertical translation of 3 units down

vertical translation of 3 units up

horizontal translation of 3 units right

horizontal translation of 3 units left

vertical translation of 3 units down

Step-by-step explanation:

we have

----> the parent function

The vertex of f(x) is the point (0,0)

----> the transformed function

The vertex  of g(x) is the point (0,-3)

so

The rule of the translation is

f(x) -----> g(x)

(0,0) ----> (0,-3)

(x,y) ----> (x,y-3)

That means ---> The translation is 3 units down

see the attached figure to better understand the problem

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12