Graph the functions y=x and y =2^x on the same graph (by plotting points if necessary). Show the points of in

Question

tersedction of these two graphs.

Answer 1

You can plot the two functions here:
http://www.coolmath.com/graphit/index.html

You can visibly see where they intersect. You can also do it with a little calculus:
Let y1 = x, y2 = 2^x, y = y2 - y1.
y1 and y2 will intersect when y1 = y2, or when y = 0.

y = y2 - y1 = 2^x - x = e^(x*ln2) - x
But notice: dy/dx = ln2*e^(x*ln2) - 1
When dy/dx = 0, ln2*e^(x*ln2) -1 = 0, so
e^(x*ln2) = 1/ln2
x*ln2 = ln(1/ln2)
x = ln(1/ln2)/ln2
Also, notice that d2y/dx2 = (ln2)^2*e(x*ln2), and when x = ln(1/ln2)/ln2, d2y/dx2 is positive. Thus, we can conclude that y is at a minimum at x = ln(1/ln2)/ln2.

But when x = ln(1/ln2)/ln2, then y = 2^x - x is positive. Since this is a minimum, we can conclude that y is always positive, and thus that 2^x is always larger than x. Thus, they don't intersect.

Answer 2

You should create an x,y chart to graph the functions. Then you'll see that they intersect at x=0 and x=1/2.

Answer 3

The two graphs do not intersect.
y = x is a straight line that has a slope o1 and passes through the origin.

y= 2^x is always positive and at - infinity and is aymptotic to the x-axis until it swings upward crossing the y axis at the oint (0,2) and shoots rapidly upwards toward + infinity. It is always above the line y=x. That should be sufficient for you to draw a rough sketch.

Answer 4

no both of them are diffirent
on is a line
and the other on is not
y=x is line
and y=2_____x is i belive a inverse s curve

i have a graphing caculator
and so i am pretty sure i am right

Answer 5

There is no point of intersection as the value of y in y = 2^x is always greater than the value of y in y=x.

Answer 6

NOT POSSIBLE..

just make the graph.. You'll find the answer.. Why are you so lazy??

Answer 7

NOT POSSIBLE.