1. Let y = 3x2 + 4x - 5
Find the y-intercept, x-intercepts, the coordinates of the vertex, and sketch the graph.
Solve 3x2 + 4x - 5 > 0 for x.
2. Solve for x
3. Graph y = 1.1x
4. Change to logarithmic form ex = a
5. Change to exponential form t = log x
7. Express as a single log: 3logb x - logb y + 4 logb z
8. Solve for x: 3x = 4x - 1
9. Solve for x: log4 (x + 3) - log4 (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.
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 23C7.
15. Compute the square root of 40.
16. Compute e2.
17. Compute ln 2.
18. Let f(x) = 3x + 4, g(x) = x2 - 3. What is
19. Let f(x) = 3x + 4. Find f -1(x). Graph both f and f -1 in the same coordinate system.