Question

Please Help .....





The figure shows the graph of the function f, defined by f(x)= |2x|+4 for all numbers x. For which of the following functions g, defined for all numbers x, does the graph of g intersect the graph of f?

A. g(x)= x-2

B. g(x)= x+3

C. g(x)= 2x-2

D. g(x)= 3x-2

Answer 1

i know the answer i just need to know how to do it please

Answer 2

I think a quick way to get the answer is to notice that the slope of f(x) = 2x + 4 is 2, while the slope of f(x) = -2x + 4 is -2. Since f(x) = |2x| + 4 is basically a composite of these functions, the new f(x) is either increasing with slope 2 or decreasing with slope -2.

To have a new linear function g(x) that is sure to intersect this function, the linear function has to be even steeper than this function, i.e. slope < -2 or slope > +2. Of your five choices, the only one meeting this requirement is E.

Answer 3

you copy and pasted this

Answer 4

yea i did

Answer 5

https://au.answers.yahoo.com/question/index?qid=20110704084502AArYawN

Answer 6

thats not helpful

Answer 7

well i believe that explains pretty well

Answer 8

i dont get it

Answer 9

i dont see what else i can add

Answer 10

so lost

Answer 11

the slope of a line tells you how "steep" it is. if the slope is a big number, it would be harder to walk up it.

from your graph

we should get the idea that some lines are too flat to ever intersect (meet) the red line

Answer 12

if that makes sense, then the next step is to figure out what is "too flat" or how steep does the line have to be ?

we know that lines with the same slope are parallel to each other
parallel means they never meet.

y= |2x| +4
for x>=0 we can drop the | | (they make the inside positive, but for x>0 it already is positives so the absolute value does nothing)
so for x>=0 y= 2x+4
any line with a slope of 2 will be parallel to this line. Choice C is
C. g(x)= 2x-2
that has slope =2. so that line never meets the y=2x+4 line
choices A and B have slopes of 1 and their y-intercepts are below the line in the graph.
so those lines have a slope that is too flat.

only choice D has a steep slope = 3 that is bigger than 2

Answer 13

hmmmm this is pretty difficult but I think i kinda get it now

Answer 14

what part is fuzzy?

Answer 15

The part about the steepness of the slope and what it has to do with the given answers.

Answer 16

do you have paper and a ruler?
draw a V shape like in your graph.
now put the ruler below the V and draw a "flat line"

If you do that, you should see that the flat line will not meet the V
now make the ruler a little more steep , and draw another line

if you keep doing that, at some point, the line you draw will meet the V

Answer 17

oh wait i re-read your explanation up there a couple times and now i got it lolol

Answer 18

once you get the idea, you next need to look at an equation of a line and see which equation has a slope bigger than 2 (which is the slope of the V)

Answer 19

Yea I see now why it's choice D. Thanks phi you're the best!