Download - AP CAB C4, C5
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Do Now
Write the following in interval notation.
1. The numbers between and including 4
and 9.
2. The numbers after 0 (not including 0) upto and including 100.
3. All positive numbers.
4. All negative numbers.
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Objectives C4 & C5AP Calculus AB
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Agenda
1. Review Do Now (5 min)
2. OBJ C4
3. Summary
4. OBJ C5
5. Summary
6. Questions
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C4: Use advanced mathematical notation to
describe properties of functions.
How we communicate the
following on the AP Test?
Domain and Range
Roots / Zeroes
Increasing or Decreasing
Concavity
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C4: Use advanced mathematical notation to
describe properties of functions.
Domain: the x values allowed by
your function.
Range: the y values allowed by
your function.
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C4: Use advanced mathematical notation to
describe properties of functions.
To find domain, it is important to
ask: What x values am I
allowed to plug into the
equation?
Most of the time, it is easier to
ask: What x can I not plug in?
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C4: Use advanced mathematical notation to
describe properties of functions.
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C4: Use advanced mathematical notation to
describe properties of functions.
To find the range, ask a similar
question: What y values can
this function give me?
Or, easier: What y values will I
never get from this function?
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C4: Use advanced mathematical notation to
describe properties of functions.
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C4: Use advanced mathematical notation to
describe properties of functions.
Roots / Zeroes
This is an incredibly important
concept in calculus. It will form
the basis for starting many
problems. They call them roots
for a reason: root of theproblem.
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C4: Use advanced mathematical notation to
describe properties of functions.
A root (aka zero) is where a
function is equal to 0. It is
located at the x values that
cause the function to be zero.
Graphically, this is where the
function crosses the x-axis.
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C4: Use advanced mathematical notation to
describe properties of functions.
Increasing and decreasing.
Many graphs in AP Calculus are
not labeled with numbers. Thismeans we need to get good a
analyzing and describing a
graph verbally.
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C4: Use advanced mathematical notation to
describe properties of functions.
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C4: Use advanced mathematical notation to
describe properties of functions.
Example:
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C4: Use advanced mathematical notation to
describe properties of functions.
Concavity:
A function is concave up when it
is a bowl open upward.
A function is concave down
when it is a bowl opendownwards.
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C4: Use advanced mathematical notation to
describe properties of functions.
Example:
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C4: Use advanced mathematical notation to
describe properties of functions.
Summary:
Precision in calculus depends
on appropriate description.
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C5: Represent a function verbally,
numerically, graphically, or algebraically.
In AP Calc, there are a number ofdifferent ways we will be interpreting
functions. Often, AP graders are less
concerned with the numbers and
more concerned with the concepts.
In addition, this is essential to critical
thinking. If you cannot think about aconcept in a new way, you dont
really understand it.
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C5: Represent a function verbally,
numerically, graphically, or algebraically.
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