Question

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)?

Answer 1

Answer:

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