Using the TI-85 graphing calculator, graphically determine which of the following functions

has larger values for **x** large.

[Press here to see animation again!]

- If you are not familiar with the graphing of functions on the TI-85, then first read the Initial Setup page from Little's Basic Guide to the TI-85.
- Press the GRAPH key and then pick
**y(x)=**by pressing the F1 key. - If necessary, keep pressing the F4 key until only
**y1=**appears on the screen. - At the prompt
**y1=**, type in**x^7**and press the ENTER key.

- At the prompt
**y2=**, type in**4^x**and press the ENTER key.

- The range settings for the graph above is
**[0, 10]**×**[0, 10**:^{6}] - Pick
**GRAPH**from the menu by pressing the F5. Since**y = x**was entered first, it is graphed first:^{7}followed by the graph of

**y = 4**:^{x} - It appears that the function
**y = x**has larger values.^{7} - However, this does not continue to happen for
**x**larger. Choose range settings**[10, 15]**×**[0, 5 × 10**; the graph of^{8}]**y = x**is^{7}and is followed by the graph of

**y = 4**:^{x} - Now it appears that the function
**y = 4**has larger values. This, in fact, can be verified by using l'Hospital's Rule.^{x}

Alternative methods for doing this type of exploration:

- Consider the graph of
**x**:^{7}- 4^{x}with viewing window

**[0, 50]**×**[-10, 10]**. - Consider the graph of
**x**:^{7}/ 4^{x}with viewing window

**[0, 50]**×**[0, 2]**.