pre-calculus 11 absolute value functions€¦ · pre-calculus 11 absolute value functions lesson...
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Pre-Calculus 11 Absolute Value Functions
Lesson Focus: To create a table of values for y = |f(x)|, given a table of values for y = f(x); to sketch the graph
of y = |f(x)| and determining its intercept(s), domain, and range; to generalize a rule for writing absolute value
functions in piecewise notation.
an absolute value function a function that involves the absolute value of a variable
i.e. 23 xy
consider the functions xxgxxf and
complete the table below for each function and then graph each function on the axes provided
consider the functions 3 and 3 22 xxhxxf
complete the table below for each function and then graph each function on the axes provided
an invariant point is a point that remains unchanged when a transformation is applied to it
it is any x-intercept of a functions before the absolute value has been applied to the function
a piecewise function is a function composed of two or more separate functions or pieces, each with its own
specific domain, that combine to define the overall function
the absolute value function y = |x| can be defined as the piecewise function
0 if ,
0 if ,
xx
xxy
the absolute value symbol is found at MATH/NUM/1 abs( on the calculator
the zero of a function 0,x is the x-value where a line crosses the x-axis (we can use our calculators by
pressing 2nd/TRACE/2)
put your cursor on the zero, press your left hand arrow 3 times, press ENTER, move your cursor back to
the zero, press your right hand arrow 3 times, press ENTER/ENTER (never Guess?)
x f(x) g(x)
-2
-1
0
1
2
x f(x) g(x)
-2
-1
0
1
2
1. How can you create a graph of
an absolute value function
from a linear function?
2. What are the domain and range
of each function?
1. How can you create a graph of
an absolute value function from
a quadratic function?
2. What are the domain and range
of each function?
e.g. Consider the absolute value function 42 xy .
1. Sketch the graph of 42 xy on the axes to the right.
2. Sketch the graph of 42 xy by reflecting all the points below
the x-axis over the x-axis.
3. Determine the y-intercept and x-intercept.
4. State the domain and range of the function.
5. What is the invariant of the transformation?
6. Express as a piecewise function.
e.g. Consider the absolute value function 322 xxy .
1. Complete the square to convert to vertex form, khxay 2
.
Sketch the graph of 322 xxy on the axes to the right.
2. Sketch the graph of 322 xxy by reflecting all the points
below the x-axis over the x-axis.
3. Determine the y-intercept and x-intercept.
4. State the domain and range of the function.
5. What are the invariants of the transformation?
6. Express as a piecewise function.