AP Precalc w/ Special Topics: Unit 1 Change in tandem

Appropriate AP reasoning for a set of data that is a function?

The relation is a function or Yes because each input has only one output

Appropriate AP reasoning for a set of data that is not a function?

The relation is not a function because not every input has exactly one in output (to take it even further),

x = (whatever input that has multiple outputs) maps to (whatever outputs is from the input)

What is not appropriate AP reasoning for whether a set of data is a function or not?

Vertical line test is not a valid explanation

What is the kind of problem that I need more practice and have a hard trouble on?

Finding graphs that represent a container (something filling up) or a situation (ex: driving between locations going, slowing down and stopping)

Interval notation

Open: ( ) Include

Closed: [ ] Don't include

When pointing out Graphical Behaviors in an interval use what

* Open intervals (use parenthesis)

because x-axis is not pos or neg. (below or above the X axis),

because we're not increasing or decreasing, positive or negative, at a distinct point, but over an interval, doesn’t stop at a specific point

In stating or picking a reason of the graph’s concavity or the rate of change (roc) decreasing or increase

Concavity and the increasing and decreasing of the roc (not positive or negative) is dependent on each other

What do you need to do with the questions on graphical behavior of functions? And the hints and help for finding it in intervals of x

Read carefully, stating a function (graph) is positive or negative (above or below x-axis) is different than stating a function (graph) is increasing or decreasing (graph’s look; “going up or down” as moving to the right or left) is different than stating the rate of change (slope) of a function is positive or negative (looks of the roc, values, of the graph), and is different from stating rate of change increasing or decreasing (of the slope; the true intention of roc (for curves))

Sometimes you need to find combinations of these above. For example, where a graph of a function is both decreasing and concave down which just find the part where the graph looks like it’s decreasing in a concave down and state the interval of where it is.

What do you need to watch for when stating intervals or actually extremas?

In the graph, endpoints instead of arrows and/or giving us restricted domains (so don’t use infinity in intervals)

POI (points of inflection)

The point where the graph changes concavity (need calculus to determine them, but some graphs might have obvious of these, which sometimes have questions of to answer)

The question of finding what is true about the graph of a function in a specific interval where the graph of the function is either a cosine or a sign having a dust main line for two cycles and having points on it.

On the AP exam, this type of question is always FRQ #3.  Of how you solve it, use the knowledge of graphical behaviors, but since it is in a different format and can’t really tell increasing or decreasing, positive or negative from the X and the Y values, look at the Y values only and answer it based on those values.

On the AP exam, what to do for rounding?

Round to 3 decimal places or truncating (just ending) after 3 decimal places

For finding what intervals the average rate of change (aroc) of a function, in the graph, is the greatest or the least?

Write the slope lines across the interval, (the most steepest if there more than one positive = greatest, Negative = least

Calculator shortcut for fraction

Alpha  y=

Calculator shortcut for getting whatever y1 is to the calculating area

Alpha Trace

For marking graph instantaneous lines, make sure what?

Draw the lines outside of the curve, so it is tangent to it, touching one point, since the instantaneous roc is the roc or slope at that one point

Slope or ROC is zero is what?

Same as (it is constant

Finding the max, min, zeros on graphing calculator

2nd Trace

—> whatever your finding

Then find the left and right boundary of the point

Linear functions has what, and so the reasoning for arguing a table is this or not

A constant average rate of change or constant 1st difference

A function is or is not a linear function because over consecutive equal length length input intervals the roc is or is not constant

Reasonings for whether a function is a quadratic or not (from a table)

Over consecutive equal length input intervals, the change in the average rate of change (the ROC of the ROC) is constant

Has a constant 2nd difference

**ROC of quadratic function can be modeled by a linear function

So… Quadratic because the average rate of change (of this table) is a linear pattern or… a function is best modeled by a quadratic function because the rate of change over consecutive equal-length input-value intervals is linear.

Reasonings for whether a function is concave up or down or neither (from a table)

Concave Up: The average rates of change over equal length input value intervals is increasing (for all small length intervals).

Concave up because the ROC is increasing

Concave Down: The average rates of change over equal length input value intervals is decreasing (for all small length intervals).

Concave down ROC is decreasing

Neither because the ROC is neither increasing or decreasing, but it is constant