Practice Exam 1

Please work out each of the given problems.  Credit will be based on the steps that you show towards the final answer.  Show your work.

Key

Problem 1  Consider the following equation

    3x² + 9x + 2  =  0

A.  Solve by completing the square

B.  Solve using the quadratic formula.

Problem 2  Calculate the discriminate and explain what it says about the nature of the roots.

    4x² - 3x -1

Problem 3  Find the equation of the quadratic with roots 2 and -1/5.

Problem 4  The graph of y = x² + 2 is shown below.  Find the equation of the other parabola.

Problem 5

Find the domain and range of 

        y  =  x² + 5

Problem 6

Which of the following functions are linear functions

A.                x
       f(x)  =       + 5
                   2

B.                 2
       g(x)  =       + 3
                    x

Problem 7

Graph 

        y  =  -|x| - 3

Problem 8

If 

        f(x)  =  x² - x        and         g(x) = 2x + 1

find

A.  gog ^-1(x)

B.  f^.g(2)

B.  gof(3)

C.  fof(x)

Problem 9

Use the graphs to find gof(1)

Problem 10

The graph of f(x) is shown below.  Sketch the graph of f ^-1(x).

Problem 11

If the graph of f(x) = b^x passes through (2,16), find f(3).

Problem 12

Write 3⁴ = 81 as a statement involving logarithms.

Problem 13

Write

        log_q (5x)  - log_q (3x - 2) as a single logarithm

Problem 14

Expand the logarithm 

                  25 x¹⁰ 
        log₅                    
                    y¹²

as much as possible and simplify.

Problem 15

Sketch the graph of y = 5^x.

Problem 16

Solve for w in 

        2^2w  =  1/256

Problem 17

When a certain radioactive element decays, the amount to the element A at any time t is given by

        A  =  25 (2^t/1500)

How much of the element will be left after 3000 years?