Find the domain of the given function. f(x) = square root of quantity x plus eight divided by quantity x plus four times quantity x minus six. f(x)=sqrt[x+8]/(x+4)(x-6)

Your f(x)=sqrt[x+8]/(x+4)(x-6) is MUCH clearer, but not 100% clear.  I will assume that your denominator here is the product of (x+4) and (x-6):

           √x+8)

f(x) =    

          (x+4)(x-6)

We cannot divide by zero.  Thus, x cannot be -4 and cannot be 6.

Thus, the domain is:

(-infinity, -4) or (-4, 6) or (6, infinity).

step-by-step explanation:

it will be a cylinder. with a diameter of 8 and 4 single pieces high

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.