Review&Sheet&Advanced&Function&Midterm&&
&
&
&
Ms.&Boyle&
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1. Simplify:&
!!!
d. 3 − 2! −6 + 5! &
a. !!!!&
!!
e. !! &
b. 3! + 6!&
c.
−9— 81&
2. Find&the&equation&of&a&line&passing&through&(3,&7)&and&(G2,&5).&
!
3. Given&the&equation&! = − ! ! + 4&
a. Find&the&slope&of&a&parallel&line&
b. Write&the&equation&of&a&parallel&line&that&passes&through&(9,&13)&
c. Find&the&slope&of&the&perpendicular&line&
d. Write&the&equation&of&a&perpendicular&line&that&passes&through&(G2,5)&
4. Factoring&fun!&&&
a. x 3 = x &
d. x 2 = 21x + 100 &
2
b. x 2 − 3x + 1 = 0 &
4 ( x − 5) = 24
e.
c. x 2 = −81 &
&
5. Determine&the&maximum&and&minimum&of&the&functions&given.&&Determine&
the&x&and&y&intercepts.&Determine&when&the&function&is&increasing&and&
decreasing.&&&Determine&the&end&behavior&of&each&function.&
1
a. y = − ( x − 4)( x + 8) &
4
2
b. y = x + 5x −14 &
c. ! = ! ! − 4!&
6. Determine&the&domain&and&range&of&each&of&the&following.&&&Determine&the&
end&behavior&of&each&function.&
!!!
€
a. ! = 3! &
c. ! = ! &
b. ! = log!&
d. ! = 2 − !&
7. Draw&a&sketch&(if&possible)&of&a&parabola&that&satisfies&the&characteristics&
below.&
a&<&0& &
&
&
c%>&0&
b
&
− &<&0&
b2 − 4ac &>&0& &
2a
8. Find&the&equation&of&a&polynomial&described:&&
a. With root −2i
b. With&a&triple&root&at&G2&and&a&double&root&at&5&that&passes&through&
(3,50)&
c. parabola&has&a&minimum&at&(G2,7)&and&passes&through&the&point&(2,&G4)&
9. Simplify:&&
a. ! !! ! &
# 15c 7 d −14 & 3
! !
d. %
( &
!
b. ! &
45c −7 d −12 '
$
!
c. 64 x−1 = 16 x +2 &
€
e.
€
€
2
7 5 = 49 4 x−3 &
f.
8 x = 26 &
i.
1
3
&
g. x = 2 &
h. x14 2 ⋅ x 7 2 ⋅ x −3 2 &
&
10. Solve:&&
a. log 3 5 9 &
€
1
b. log x 3 = &
4
c. log x (3 − 4 x) = 2 &
€
3
d. log x 27 = &
2
€
j.
€
100 x = 10 x + 6 &
" 1 %−3
$ '
#4&
1
1
log 81− log 27 &
2
3
log 7 x + log 7 ( x − 6 ) = 1 &
e. log x =
f.
g. log 7 x = 4 log 7 2 + ( log 7 3 − log 7 6 )
€
!
11. Given&! ! = !!!,&! ! = !,&and&ℎ ! = ! ! &
a. find&the&domain&of&f(x),%
d. find&h(g x )&
g(x),%and&h(x)&
e. find&the&domain&of&each&
b. find&f(g x )&
of&the&composite&you&
c. find&f(h x )&
found&
12. Given&! ! = !.&&
a. find&the&domain&and&
c. find&the&domain&and&
range&of&g(x).&
range&of&&!!! (!)&
b. find&!!! (!)&
13. Sketch&the&piecewise&functions&
! + 2,!!!!!!! < 3
! ! + 1,!!!!!!! > 0
a. ! ! =
&&
b. ! ! =
&
!!
7 − ! ,!!!!! ≥ 3
1 − 4!,!!!!!! < 0
14. Sketch&the&transformations&of&the&original&function.&&Note&these&building&on&
each&other.&&&
a. ! ! − 1&
b. – ! ! − 1
!
c. − ! ! ! − 1
&
&
&
&
Be&prepared&to&classify&a&function,&find&the&x&and&y&
intercepts,&local&maximums&and&minimums,&and&
determine&when&the&function&is&increasing&and&
decreasing.&&
&
Be&prepared&to&know&the&relationship&between&degree&of&a&function&and&the&number&
of&zeros&or&maximums&and&minimums&a&function&has.&&&