Originally Posted by

**pickslides** Lets start with these two parts. With these points $\displaystyle x=2,1,0.5,0.1,0.01,0.001$ one at a time compare them to the y-intercept (x=0) like this

x=0: gives $\displaystyle -3(1/2)^{(0)-2}+6=\dots $ what do you get?

x=2: gives $\displaystyle -3(1/2)^{(2)-2}+6=\dots $ what do you get?

x=1: gives $\displaystyle -3(1/2)^{(1)-2}+6=\dots $ what do you get?

x=0.5: gives $\displaystyle -3(1/2)^{(0.5)-2}+6=\dots $ what do you get?

and so on....

then draw the lines connecting

$\displaystyle (0, f(0))$ and $\displaystyle (2, f(2)) $

$\displaystyle (0, f(0))$ and $\displaystyle (1, f(1)) $

$\displaystyle (0, f(0))$ and $\displaystyle (0.5, f(0.5)) $

and so on...

Then find the equation of the straight line between each of these pairs.

What do you notice about the gradient of these lines as $\displaystyle x$ gets very small?