Graphical Reasoning...4

[nycmathguy]

Section 1.8
Question 28

For this question, I want you to graph f, g and f + g but let me answer the question. Use a different color for each graph.

See attachment.

 

[MathLover1]

28.

 

[nycmathguy]

28.

I will use algebra again.

Let x = 1.

f(1) = 1^2 - 1/2 or 1/2.

g(1) = -3(1)^2 - 1 or -4.

I know that 1/2 > -4.

I say f(x) is above g(x) for 0 <= x <= 2.

Let x = 7.

f(7) = 7^2 - 1/2 = 49 - 1/2 or 48.5.

g(7) = -3(7)^2 - 1 = -3(49) - 1 or -148.

Since 48.5 > -148, I conclude that f(x) is above g(x) on the xy-plane when x > 6.

Yes?