Graphical Reasoning

[nycmathguy]

Section 1.8
Question 26

See attachment.

I know how to graph f, g and f + g on the same xy-plane.

Explain the following:

Which function contributes most to the
magnitude of the sum when 0 ≤ x ≤ 2?
Which function contributes most to the
magnitude of the sum when x > 6?

 

[MathLover1]

Which function contributes most to the
magnitude of the sum when 0 ≤ x ≤ 2?

the orange line ( g(x)=sqrt(x)) contributes more when 0 ≤ x ≤ 2

Which function contributes most to the
magnitude of the sum when x > 6?

blue line (f(x)=x/2) contributes most when x > 6

 

[nycmathguy]

View attachment 227

Which function contributes most to the
magnitude of the sum when 0 ≤ x ≤ 2?

the orange line ( g(x)=sqrt(x)) contributes more when 0 ≤ x ≤ 2

Which function contributes most to the
magnitude of the sum when x > 6?

blue line (f(x)=x/2) contributes most when x > 6

Sorry but I don't get it.

 

[MathLover1]

green line is the sum function f + g=(1/2)x+sqrt(x)
the magnitude of the sum are y values (distance from x-axis(

function contributes most to the magnitude of the sum when 0 ≤ x ≤ 2 is orange line ( g(x)=sqrt(x)) because
orange line is above blue line which means y values of g(x)=sqrt(x) are greater than y values of f(x)=(1/2)x in interval [0,2]

and blue line (f(x)=x/2) contributes most when x > 6 because blue line is above orange line which means y values of f(x)=(1/2)x are greater than y values of g(x)=sqrt(x) in interval (6,infinity]

 

[nycmathguy]

green line is the sum function f + g=(1/2)x+sqrt(x)
the magnitude of the sum are y values (distance from x-axis(

function contributes most to the magnitude of the sum when 0 ≤ x ≤ 2 is orange line ( g(x)=sqrt(x)) because
orange line is above blue line which means y values of g(x)=sqrt(x) are greater than y values of f(x)=(1/2)x in interval [0,2]

and blue line (f(x)=x/2) contributes most when x > 6 because blue line is above orange line which means y values of f(x)=(1/2)x are greater than y values of g(x)=sqrt(x) in interval (6,infinity]

1. Green line is the sum of the two functions.

2. The blue line is above the orange line for values where x is greater than 6.

Yes?

I will do a few more and post my work when time allows.

 

[MathLover1]

Yes

 

[nycmathguy]

Yes

I will work on two more when time allows and show my work.