Suppose that f(x) = x^2 and g(x) = 2/3x^2. which statement best compares the graph of g(x) with the graph of f(x)?
a.) the graph of g(x) is the graph of f(x) compressed vertically.
b.) the graph of g(x) is the graph of f(x) stretched vertically and flipped over the x-axis.
c.) the graph of g(x) is the graph of f(x) stretched vertically.
d.) the graph of g(x) is the graph of f(x) compressed vertically and flipped over the x-axis

Multiplying a function by a number that when squared is less than one, compresses the graph vertically by a factor equal to the coefficient.

In this case (2/3)^2=4/9 and 4/9<1 so the graph of G(x) is the graph of F(x) compressed vertically.

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