SOLUTION: how do the graphs of f(x)=x^2 + x and g(x)= x^2+|x| compare? A. f(x)=g(x) for x<0 B. f(x)>g(x) for x<0 C. f(x)=g(x) for x> or equal to 0 D. f(x)> g(x) for x> or equal to 0

Question 253390: how do the graphs of f(x)=x^2 + x and g(x)= x^2+|x| compare?
A. f(x)=g(x) for x<0
B. f(x)>g(x) for x<0
C. f(x)=g(x) for x> or equal to 0
D. f(x)> g(x) for x> or equal to 0
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
I would say selection c.

when x < 0, f(x) < g(x) so selection a is false.
when x < 0, f(x) < g(x) so selection b is false.
when x >= 0 f(x) = g(x) so selection c looks good since |x| = x when x >= 0
when x >= 0 f(x) = g(x) so selection d is false.

graph of both equations looks like this:

you can see that when x >= 0 it looks like one graph.

this is because the 2 equations are identical and become superimposed on each other.

when x is negative, the graphs are separate.

the red graph (the lower one) is the equation f(x) = x^2 + x.

the green graph (the higher one) is the equation f(x) = x^2 + |x|

as an example:

when x = -8, x^2 + x becomes 64 - 8 = 56

when x = -8 x^2 + |x| becomes 64 + 8 = 72

I drew horizontal lines at y = 56 and y = 72 so you could see that easier.

find x = -8 and trace vertically up until you see the intersection points.

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