Directions: Show your work for credit. Write all responses on separate paper. Do not abuse a calculator.
1. Find
an equation for the linear function tabulated below.
x |
1 |
2 |
4 |
11 |
y |
1.21 |
2.42 |
4.84 |
13.31 |
2. Make a table of values and sketch a graph for the function
3.
Find a formula for the cubic (third degree)
polynomial whose graph is shown at right. 4.
Julie leaves her house and walks 200 feet (her
walking speed is 2 feet per second) down the street to the bus stop where she
waits 100 seconds for the bus. The bus
drives 26.8 miles per hour back down the street past her house to a location
3000 feet down the same street in the other direction. Sketch a graph for the function that
describes Julies’ distance from her house (in feet) as a function of time (in
seconds.) 5. The function has a maximum value at (0,1) and is asymptotic to the x-axis. |
a. Write a formula for without using function notation (f).
b. What transformation of f will move the maximum from (0,1) to (2,5) while leaving the horizontal asymptote intact.
c.
What transformations of f will produce the graph below?
6. Find
a formula for the inverse function of .
Make a table of values including 3 or 4 points on the curve and then graph and together in the same coordinate plane showing
the symmetry through the line y = x.
7. Consider and .
a. What is the domain of the composition ?
b. What is the range of the composition ?
8. Write
as the function of a positive angle less than
2π in the first quadrant.
9. Eliminate
the parameter from the parametric equations
to get a Cartesian equation. How should
you limit the domain and range of the Cartesian equation to make it equivalent
to the parametric equations.
10. Write a
parameterization of the ellipse with Cartesian equation starting at ( 2,
1)
and tracing the ellipse once in the clockwise direction.