### MATH100 Sample Final

This is a sample final exam. The questions on the actual final exam may or may not be similar to these; these questions are similar to problems that might appear on the final (although sample problems are often more difficult than those on the final).

1. Shown above is the graph of a function g(x). Use the graph to find approximate solutions to the equation g(x) = 2.

2. Shown above is the graph of a function g(x). For what values of x is the function g(x) increasing?

3. Give the equation of the line that passes through the point (2,3) and is perpendicular to the line y = 1/2 x + 1.

4. Solve for x: | x - 3 | < 1.

5. Sketch the graph of the piecewise defined function:
 f(x) = x² 0 < x < 1 x x > 1

6. Give the equation of a function whose graph is a parabola that opens downward from its vertex at (3,4).

7. Are the functions f(x) = 2/x and g(x) = 2x inverses of each other? Justify your answer.

8. Give the equation of a third degree polynomial function that has x-intercepts (0,0), (1,0) and (2,0). You may leave your answer in factored form.

9. Describe all the vertical, horizontal or slant asymptotes of the graph of the function
h(x) = (x² - 4)/(x² - 2x - 3).

10. If log2(x) = 4, what is x?