You have two exponential functions. one function has the formula g(x) = 3 x . the other function has the formula h(x) = 2-x . which option below shows the graph of k(x) = (g - h)(x)?

see graph

Step-by-step explanation:

g(x) = 3^ x .

h(x) = 2^-x

We want to subtract them

f(x) = 3^x - 2^(-x)

I will rewrite without the negative exponent

f(x) = 3^x - (1/2)^(x)

Lets pick a couple of points

f(0)  = 3^0 - (1/2) ^ 0 = 1-1 = 0

As x gets large 3^x gets large and 1/2^x gets close to 0, so it will get large

As x goes to negative infinity, 3^x goes to zero and 1/2^ gets large  so we get - infinitity

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