AP Precalculus Exam Prep
1. The a in g(x)=aÅf (b(x-h))+k Vertical dilation by a factor of a
Reflection over x-axis if a <0
2. The h in g(x)=aÅf (b(x-h))±k Horizontal translation
Left when x+h, Right when x-h
3. The k in g(x)=aÅf (b(x±h))+k vertical translation
Up when k>0, Down when k<0
4. The b in g(x)=aÅf (b(x±h))+k Horizontal dilation by a factor of 1/b
Reflection over y-axis if b<0
5. Average Rate of Change Formula f(b)-f(a)
b-a
6. Where is a function positive/neg- Å
Positive-when the y-coordinates are
ative? above
the x-axis [ positive]
ÅNegative when the y-coordinates are
below
the x-axis [negative]
7. What defines an increasing/de- IÅncreasing when the outputs increase
creasing as the
function? inputs increase [ROC/slope positive]
ÅDecreasing when the outputs decrease
as the
inputs increase [ROC/slope negative]
8. What is a Point of Inflection? The ordered pair where concavity
changes.
9. What justifies an increasing rate When a function is concave up
of change?
, AP Precalculus Exam Prep
10. What justifies a decreasing rate of When a function is concave down
change?
11. What does it mean if c is odd in cÅ is a zero with odd multiplicity
f(x)=a(x-b)^c? Åthe graph of f will cross the x-axis at x=c
--> if c = 1, will cross linearly
--> if c = 3, will cross like a cubic function
(x-int will be point of inflection]
12. What does it mean if c is even in cÅ is a zero with even multiplicity
f(x)=a(x-b)^c? Åthe graph of f will touch the x-axis and
turn at x=c [bounce]
13. What is an even function? Å hen f(-x) = f(x)
W
ÅOpposite input values have the same
output values
Åsymmetric about y-axis
14. What is an odd function? fÅ(-x) = -f(x)
ÅOpposite input values have opposite
output values
Åsymmetric about origin
15. Notation for end behavior as in- lim f(x)
puts decrease without bound x->-
16. Notation for end behavior as in- lim f(x)
puts increase without bound x->
17. Horizontal asymptote test when: Åif n<m, H.A. at y=0 (bottom heavy(
nth degree polynomial Å if n=m, H.A. at
r(x)= --------------------------- L.C of numerator
mth degree polynomial y= ---------------------
L.C of denominator
Å if n>m, no H.A. (top heavy)
, AP Precalculus Exam Prep
18. When does a rational function ÅWhen the degree of the poly in the
have an oblique asymptote? numerator is greater than the degree of
the poly in the denominator
Å use division [reverse box] to calculate
oblique asymptote
19. Where does a rational function ÅWhen a factor cancels in the numerator
have a hole? and denominator (unless covered by a
V.A. --> factor still remains in denomina-
tor)
ÅLet f(x) be a polynomial in numerator
and g(x) be polynomial in denominator.
Hole occurs at x = a if a is a zero of
BOTH f(x) and g(x)
20. Where does a function have a ÅWhen a factor is a zero of the denomi-
V.A.? nator after canceling
ÅLet f(x) be a polynomial in numerator
and g(x) be polynomial in denominator.
VA occurs at x = a if a is a zero of only
g(x) [after canceling]
21. Standard form of arithmetic se- an=ak+d(n-k) where (k, ak) is any or-
quence dered pair in the sequence
22. Standard form of geometric se- gn=gkÅ r^n-k where (k, gk) is any or-
quence dered pair in the sequence
1. The a in g(x)=aÅf (b(x-h))+k Vertical dilation by a factor of a
Reflection over x-axis if a <0
2. The h in g(x)=aÅf (b(x-h))±k Horizontal translation
Left when x+h, Right when x-h
3. The k in g(x)=aÅf (b(x±h))+k vertical translation
Up when k>0, Down when k<0
4. The b in g(x)=aÅf (b(x±h))+k Horizontal dilation by a factor of 1/b
Reflection over y-axis if b<0
5. Average Rate of Change Formula f(b)-f(a)
b-a
6. Where is a function positive/neg- Å
Positive-when the y-coordinates are
ative? above
the x-axis [ positive]
ÅNegative when the y-coordinates are
below
the x-axis [negative]
7. What defines an increasing/de- IÅncreasing when the outputs increase
creasing as the
function? inputs increase [ROC/slope positive]
ÅDecreasing when the outputs decrease
as the
inputs increase [ROC/slope negative]
8. What is a Point of Inflection? The ordered pair where concavity
changes.
9. What justifies an increasing rate When a function is concave up
of change?
, AP Precalculus Exam Prep
10. What justifies a decreasing rate of When a function is concave down
change?
11. What does it mean if c is odd in cÅ is a zero with odd multiplicity
f(x)=a(x-b)^c? Åthe graph of f will cross the x-axis at x=c
--> if c = 1, will cross linearly
--> if c = 3, will cross like a cubic function
(x-int will be point of inflection]
12. What does it mean if c is even in cÅ is a zero with even multiplicity
f(x)=a(x-b)^c? Åthe graph of f will touch the x-axis and
turn at x=c [bounce]
13. What is an even function? Å hen f(-x) = f(x)
W
ÅOpposite input values have the same
output values
Åsymmetric about y-axis
14. What is an odd function? fÅ(-x) = -f(x)
ÅOpposite input values have opposite
output values
Åsymmetric about origin
15. Notation for end behavior as in- lim f(x)
puts decrease without bound x->-
16. Notation for end behavior as in- lim f(x)
puts increase without bound x->
17. Horizontal asymptote test when: Åif n<m, H.A. at y=0 (bottom heavy(
nth degree polynomial Å if n=m, H.A. at
r(x)= --------------------------- L.C of numerator
mth degree polynomial y= ---------------------
L.C of denominator
Å if n>m, no H.A. (top heavy)
, AP Precalculus Exam Prep
18. When does a rational function ÅWhen the degree of the poly in the
have an oblique asymptote? numerator is greater than the degree of
the poly in the denominator
Å use division [reverse box] to calculate
oblique asymptote
19. Where does a rational function ÅWhen a factor cancels in the numerator
have a hole? and denominator (unless covered by a
V.A. --> factor still remains in denomina-
tor)
ÅLet f(x) be a polynomial in numerator
and g(x) be polynomial in denominator.
Hole occurs at x = a if a is a zero of
BOTH f(x) and g(x)
20. Where does a function have a ÅWhen a factor is a zero of the denomi-
V.A.? nator after canceling
ÅLet f(x) be a polynomial in numerator
and g(x) be polynomial in denominator.
VA occurs at x = a if a is a zero of only
g(x) [after canceling]
21. Standard form of arithmetic se- an=ak+d(n-k) where (k, ak) is any or-
quence dered pair in the sequence
22. Standard form of geometric se- gn=gkÅ r^n-k where (k, gk) is any or-
quence dered pair in the sequence
