Unit 1 AP Precalculus

When Graph Concaves Up

AROC is Increasing

When Graph Concaves Down

AROC is Decreasing

Positive ROC (Rate of Change)

When both quantities on the x and y axis increase

Negative ROC (Rate of Change)

When y-value increases and x-value decreases

Even Function

Symmetric over the line x = 0 and satisfies the property f(-x) = f(x)

Odd Function

Symmetric over the point (0, 0) and satisfies the property f(-x) = -f(x)

AROC

Y2-Y1 / X2-X1

Rate of Change Positive

Graph is Increasing

Rate of Change Negative

Graph is Decreasing

IROC

Find Tangent Line and Do f(b) - f(a) / b - a

Change in AROC for Linear Functions

0

Change in AROC of Quadratic Functions

Constant

POI (Point of Inflection)

X = b - a | Y = f(b) - f(a)

Odd Multiplicity

Cross the X-axis

Even Multiplicity

Touch/Bounce Off the X-axis

If (a + √b) is a Zero, then

(a -  √b) is a Zero

If (a + bi) is a Zero, then

(a - bi) is a Zero

Relative / Local Extrema

Y-values on graph change from increasing to decreasing or vise versa.  OR and endpoint when the domain is restricted.

Absolute / Global Extrema

The highest / lowest local extrema so long as the graph does not continue forever.