Download Assignment - Absolute Value and Reciprocal Functions

Math 20-1 Assignment
Absolute Value Functions and Reciprocal Functions
Name: ______________________________
Date: ________________
1. Write the following as piecewise functions, and graph each function:

y  3x  9

y 
1
x  22  3
3
2. Given: p  1  p  1

Algebraically determine the solution(s) to this equation.
Solution #1
p  1  p 1

Solution #2
p  1  p 1
Demonstrate the verifications of your solutions algebraically.
3. Consider:
x2  4  x  2

Write y  x 2  4 in piecewise notation.

Algebraically determine the solution to x 2  4   x  2
Solution #1
x2  4  x  2

Solution #2
x2  4  x  2
Demonstrate the verifications of your solutions algebraically.
4. Solve:
3x  5  x  2  2 x  3
5. The launch window for a satellite is the set of times within which it must be launched to meet
its objectives. The launch window for a new weather satellite is represented by the
inequality: t  360  20 where time is in minutes from the start of the countdown to the
launch. If the countdown starts at 01:00 hrs, what are the maximum and minimum times for
which this satellite can be launched? Record your solution in h:min. (2 marks)
1
is shown to the right.
f x 
State the equations of the horizontal and vertical
asymptotes of the reciprocal graph and label them
on the graph. (The asymptotes are integer values)
6. The graph of y 


Identify and label the locations of the invariant
1
points between y  f x  and y 
f x 

Use the graph to determine the x and y intercepts of
the graph of y  f x  .

Use your knowledge of reciprocal functions to determine the equation of y  f x 
(Hint: y  mx  b )