Question

The functions f(x) and g(x) are shown below:

f(x) = 2x
g(x) = 2x

Which statement best describes the graph of f(x) and g(x)?

Answer 1

Please help!

Answer 2

The graph of f(x) will eventually exceed the graph of g(x)
The graph of g(x) will eventually exceed the graph of f(x0

Answer 3

Both will have their y-intercept equal 1
Both will have their y-intercept equal 2

Answer 4

f(x) and g(x) look identical. Is there a typo?

Answer 5

Yeah sorry f(x)^2

Answer 6

so f(x) = x^2 ?

Answer 7

yeah :)

Answer 8

g(x) is 2x ?

Answer 9

yep

Answer 10

ok let's graph the two functions

I used https://www.desmos.com/calculator

Answer 11

x^2 is the red curve
2x is the blue line

Answer 12

Oh! okay.

Answer 13

So what i am looking for is where they intersect?

Answer 14

so you can see which graph eventually wins in terms of larger y values

Answer 15

ohh! okay soo.. blue line right?

Answer 16

which is g(x)

Answer 17

see how the red curve is above the blue line when x > 2 ?

Answer 18

yeah

Answer 19

so f(x) overtakes g(x) and it stays that way forever when x > 2

Answer 20

oh! i understand

Answer 21

so then it would be the first option correct?

Answer 22

yes

Answer 23

g(x) is only larger than f(x) for a very brief point in time (when 0 < x < 2)

the rest of the time, f(x) is larger

Answer 24

I see.. okay
Thank you! Jim_Thompson5910

Answer 25

you're welcome