1. Let *y* = 3*x*^{2} + 4*x* - 5

Find the *y*-intercept, *x*-intercepts, the coordinates of the vertex,
and sketch the graph.

Solve 3*x*^{2} + 4*x* - 5 __>__ 0 for *x*.

2. Solve for *x*

3. Graph *y* = 1.1^{x}

4. Change to logarithmic form
*e ^{x}* =

5. Change to exponential form *t* = log *x*

6. Expand

7. Express as a single log:
3log_{b} *x* - log_{b} *y* + 4 log_{b} *z*

8. Solve for *x*: 3^{x} = 4^{x - 1}

9. Solve for *x*: log_{4} (*x* + 3) -
log_{4} (*x* - 1) = 1

10. Suppose that the population of a city is 10,000 in 1970 and 50,000 in 1990. Assume further that the population is given by the formula

where *P* is the population in the year 1970, *t* is the number of
years since 1970, and *r* is a suitable constant.

- a) Find the value of
*r*which will explain this data. - b) Use this value of
*r*to predict the population in year 2000 - c) In what year will the population reach 100,000?

11. The half life of a radioactive substance is 2.3 years. Scientists figure that it will be safe to handle it if there is only 10% of the radioactivity left. How long would one have to wait until it was deemed safe?

12. Write out Pascal's triangle to the 7th row.

13. Remove parentheses and simplify (*x* + *y*)^{6}.

14. Compute _{23}C_{7}.

15. Compute the square root of 40.

16. Compute *e*^{2.}

17. Compute ln 2.

18. Let *f*(*x*) = 3*x* + 4, *g*(*x*) = *x*^{2} - 3. What is

*(f + g*)(*x)*- (
*f*-*g*)(*x*) - (
*fg*)(*x*) - (
*f/g*)(*x*) - (
*f*o*g*)(*x*) - (
*f*o*g*)(*x*)

19. Let *f*(*x*) = 3*x* + 4. Find *f* ^{-1}(*x*). Graph both *f* and *f* ^{-1} in the same coordinate system.