Question

What is the graph of the rational function y = 2x + 4/x+1

Answer 1

See attachment for your answer;

Answer 2

The answer is in the attachment.

Explanation:

When x is much greater than 0 then 4/x tends to 0 and y =2x + 4/x + 1 tends to y =2x + 1.

For example, for x = 100:

• f(x) = 2x + 4/x+1 = y(100) = 2*100 + 4/100 + 1 = 200 + 0.04 + 1 = 201.04

• f(x) = 2x + 1 = y(100) = 2*100 + 1 = 200 + 0.04 + 1 = 201

When x aproximates to 0 then 4/x tends to ∞ and y =2x + 4/x + 1 tends to ∞ .

For example, for x = 0.001:

• f(x) = 2x + 4/x+1 = y(0.001) = 2*0.01 + 4/0.001 + 1 = 0.002 + 4000 + 1 = 4001.002

When x = 0 then 4/x have no solution because a number can not be divided by 0 and you have a discontinuity in this function at this point .