## First Midterm

## Summer Session 2000

1. The population of a town was 20,000
in 1970, and 40,000 in 2000. Let x denote the number of years from
1970, and let y denote the population. Find a linear equation which
predicts these population figures. Use this equation to predict the
population in 2010.

2. In Problem 1, find an exponential
function which predicts the figures. Use this exponential function to
predict the population in 2010.

3. Graph y = x^{2} + 2x - 3.
Find

- the y-intercept
- the roots
- the coordinates of the vertex

4. Solve x^{2} + 2x - 3 > 0

5. Let f(x) = 2x + 3, g(x) =
x^{2} + 2x. Find fog(x) and gof(x).

6. Let

find f^{-1}(x).

7. Expand

8. Express as a single log

2ln a + 3ln b - ln c
9. Solve for x and check:

log_{12}x + log_{12}(x + 1) = 1
10. Graph

Find

- the y-intercept
- the roots
- the vertical asymptotes
- any horizontal asymptotes
- (extra credit: the vertices)

11. This is the graph of y = f(x).

Match the following functions with their graphs.

a) f(x + 2), b) f(x - 2), c) f(x) + 2, d) f(x) - 2, e) f(2x), f) f(x/2), g) 2f(x), h) f(x)/2