If the parent function is y = x, explain the transformation(s) that occur to get from the parent function to y = 3(x - 5) – 2

Going from y = x to y = 3x means we have vertically stretched everything by a factor of 3. For example, the point (4,4) moves to (4,12).

Then we replace x with (x-5) so that we get to y = 3(x-5). This shifts the graph 5 units to the right.

Finally, the -2 at the end shifts everything down 2 units.

Summary:

We applied these three transformations

Vertically stretch by a factor of 3Shift 5 units to the right.Shift 2 units down

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