Book Review #s 51 and 52

These problems were kind of difficult for me, so I spent a lot of time thinking about them. Just thought I'd share some ideas...

For 51, I figured that as x went up, y would go down (since it's -logbaseb(x)). At first I thought it would be a regular concave up exponential growth graph except reflected over the x-axis. So I thought it was graph VI. Then I realized x must be greater than 0, so it had to be graph V.

For 52 I had a harder time... as x gets bigger in the positive direction, y gets smaller (if you take b - a fraction - to the millionth root it's smaller than taking it to the third root). As x gets bigger in the negative direction, y gets bigger (b to the negative million is 1/(b^1000000), which 1 over a really small fraction... basically a really big number). So graph IV is the only one that seems reasonable. Also... you know that when x=0, g(x) must equal 2. 2 is the y-intercept of graph IV, so it all works out!