Download Absolute Value Equations and Inequalities

Precalculus Summer Assignment Assistance
#1: Absolute Value Equations and Inequalities
Draw number lines to help answer the following questions, then try to come up with an
algebraic approach that will work with more complicated problems.
1. If x  5 , what are the two possible solutions for x? This equation, x  5 , is asking
“What numbers are five units away from 0?”
2. If x  2  1 , what are the two possible solutions for x? This equation, x  2  1 , is
asking “What numbers are 1 unit away from 2?”
3. If x  4  3 , what are the two possible solutions for x? This equation, x  4  3 , is
asking “What numbers are 3 units away from -4?”
4. If x  1  5 , there are infinitely many solutions but we must describe them. This
inequality, x  1  5 , is asking “What numbers are more than 5 units away from 1?”
5. If x  6  8 , there are infinitely many solutions but we must describe them. This
inequality, x  6  8 , is asking “What numbers are less than 8 units away from -6?”
Overall: Interval notation for a solution set that has an infinite number.
(smallest #, largest #) neither endpoint is included as a solution but every number in
between is a solution
[smallest #, largest #] both endpoints are included as a solution and every number in
between is a solution
[smallest #, largest #) smallest endpoint is a solution but the largest endpoint is not and
every number in between is a solution
(smallest #, largest #] I think you can guess at what this represents from the above
explanations. If you are not sure, talk to me.
#3, #10: Writing linear equations
Find the slope, either from rise over run, the formula, or identifying a parallel (same) or
perpendicular (opposite, reciprocal) slope from a given line.
Next, plug the slope and a known ordered pair into y=mx+b to solve for b.
Last, rewrite your equation now that you have m and b.
#17: Vertical motion
 s(t) stands for the position of the object at any time, t.
 vo stands for the initial velocity of the object at the beginning of the problem
 so stands for the initial position of the object at the beginning of the problem
 t is time in seconds
Why -16???
Plug in everything you know for the appropriate variable and solve for what the questions
ask for. You may do this algebraically or on your graphing calculator. I suggest doing
both!!!!
#8: Domain of square root functions
Think about what kind of numbers are allowed or not allowed under a square root. Now
set up an inequality/equation to make this happen.
1. x
2. x  4
x  0 or [0, ∞)
x  4  0 → x  4 or [4, ∞)
#9: Domain of rational functions
A rational function is a fraction. What causes major problems in fractions?
Write an equation to find when this problem will happen and eliminate that from the
domain.
3
f(x)=
x≠0 so (-∞, 0)  (0, ∞)
x
#16: Piecewise functions
Decide which piece the particular x-value belongs in, plug in to that piece of the function
ONLY.