The rational function f(x)=4x+16/ X+2 is in quotient form.

a. Use long division to rewrite the function f(x) in transformation form (as a transformation of y= 1 E).

b. Using your answer to part a, sketch the graph of f(x) and describe how it is a transformation of the graph of y=1/x

c. Does the graph of f(x) have any vertical or horizontal asymptotes? If so, where?

d. How is the graph of f(a) the same and/or different from the graph of r(x)= 4x^2+20x+16/ x^2+3x+2

in simplified version   it would be x ≤-4

step-by-step explanation:

multiply each term in x ≤-4 by -1

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.