AP Pre-Calc Unit 1

Relative Min/Max

When you can not go down any further (includes all the vertex + Absolute min/max)

- Switches from increasing to decreasing or vice versa (turning points)

Absolute Min/Max or Endpoints

Range, the highest or lowest points

the global end

Domain

what x can be, everything but the restrictions

Range

What y can be

even symmetry

f(x) = f(-x), both sides end in the same direction

odd symmetry

f(-x)=-f(x)

symmetric about origin, graph ends in different directions

increasing on an interval

f(x1) < f(x2)

decreasing on an interval

f(x1) > f(x2)

constant

f(x1) = f(x2)

secant line

the average rate of change of a function from A to B equals the slope of that distance's secant line containing the two points

(a, f(a)) and (b, f(b)).

End behavior even degree

negative leading coefficient: f(x) = positive infinity

positive leading coefficient: f(x) = negative infinity

EVEN DEGREE LIM NOTATION IS THE SAME FOR BOTH INFINITY

point of inflection

where the graph changes from increasing to decreasing (or vice versa), goes from concave down to concave up (in the middle of the lines)

how to find secant line with a given interval

plug in the numbers and calculate the slope, put that slope back into the mx + b = y equation to figure out the secant line

Horizontal Asymptote

when lim x = infinity, f(x) = the value of the HA

numerator degree bigger than denom degree: none

Num degree smaller than denom degree: y=0

degrees equal: take the coefficients

Oblique asymptote

when the tope degree is greater than the bottom by one, go off to infinity

Zeros

numerator is equal to zero and is not crossed out

domain restrictions

when the denominator is equal to zero

vertical asymptote

what makes the denominator 0 (x =) and does not cross out

Holes

x crosses out and y is x plugged back in

VA End behavior

lim x goes to left and right side of the VA. f(x) = -+ infinity depending on number line/graph

Hole End behavior

lim x = the hole's x value and the f(x) = the hole's y value

y=f(x) + c

up c, effects the Range

y = f(x) - c

down c, R

y = f(x+c)

left c, D

y = (f-c)

right c, D

y= kf(x)

multiply y by k, R

y = f(kx)

multiply x by 1/k, D

y = -f(x)

reflect across x-axis, R

y = f(-x)

reflect across y-axis, D

y = |f(x)|

( x value, always positive y-value), R

y = f(|x|)

(always positive x value, y-value), D and R