Math 1A

 Chapter 1 Test Solutions

Directions: Show your work for credit.  Write all responses on separate paper. Do not abuse a calculator.

x	1	2	4	11
y	1.21	2.42	4.84	13.31

 

1.      The linear function tabulated below represent a sampling of y = 1.21x.

 

x 0 1 2 3 4 y 1 0 1 2 1 2.      Here’s a table of values and a sketch for the graph for the function

 

3.      The cubic (third degree) polynomial whose graph is shown at right is described by 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 12.8 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 parametrization of the ellipse with Cartesian equation  starting at ( 2, 1) and tracing the ellipse once in the clockwise direction.