Hello, geton!
2. a) Sketch the graph of:
On the same axes, sketch the graphs of: .
Show the coordinates of the points where the graph meets the axes. Code:

* 
* 
* *½ *
*  * *
*  * 1 *
**
0 *
 *
 *
   1+          

We're expected to be familiar with the graph of
The graph of is a reflection of (a) over the yaxis.
The graph of is the graph of (b) lowered one unit.
The two lines intersect at (1,0) and exist above the xaxis.
The intercepts are: . 0,\,0),\;(1,\,0),\;\left(0,\,\frac{1}{2}\right)" alt="\0,\,0),\;(1,\,0),\;\left(0,\,\frac{1}{2}\right)" />
The only intersection is that of: .
We have: .
Therefore, is a root of: .
c) Show that: .
Since both the exponential function and the line are continuous,
. . the most elementary method is to test the endpoints.
At . . . the exponential is above the line
At . . . the exponential is below the line
Therefore, they intersect somewhere on the interval