~
Test Review: Periodic Functions
The test will be no calculator, so for the best practice, complete this review without the aid of a calcul?t-:!: _
Desmos.
3,/L - 2 x'- I ::: o-1,iJ\-:: .!, s )
1
*
1. Select all that are solutions to the following equation. .Vl )(.~J.J
(x-, ..3 :::1!:.r.uc.-l
eoe= TT-~( .1. \ )
2
3 tan 0 - 2 tan 0 - 1 = o x- 1 _ , " J2 s
- - - - - -J - ~ ·--- f7-4'c:Aatt ( °i
: arctan(½)
TC - arctan (½)
5 ;,,2. + , ~ .:.. .i r. 6 - (- o•
~o.n 1.-+- \ ::: tec.1- J(l--co~')tl + .1l'o'S :
2.
1.,. to-t:'I.::: c:..sc'2- 3 -3Gof"'8 +5"to5S-( -o
serecr dll that are solutipps to the following equation.
<o, -.n -l fi" noel l\a➔ 1. 2 + cos 0 - o
sm 0 -
. 1 -
3
5
arccos(2) {rr-- arccos (i)) 2TC - arccos (½) 1
2TC + arccos (½)
TC - arccos(2) arccos (½) 2TC - ar;cos(2) ___: eOS (½[I •
Use the below table of f(x), graph of g(x), and equation of h(x) to answer #3-9
4
3 X -3 -2 -1 0 1 2 3
f(x) 2 1 3 0 -3 -2 -1
2
-
2 3 4
-1 h(x) = 3x - 6
-2
-3
-4
4. Find f- 1 (-3)
.L
9. Find on expression for h- 1 (x)
'd::. 3x - b
f:zjy
CBHS AP Precalculus 2025/26 - Periodic Graphs, Test Review (Day 12)
, (x) be the periodic function tor which y = f (x) is graphed below. Use this question to answer #10-13.
5
4,
3
2
I
.. 2 -1 oI 3 5
-3
10. What is the period off (x)?
2-
11. What is the amplitude off (x)?
lf r
-5
or,;i" r.:JMM~
12. Let g(x) = 2f(x - 1) + 3.
What is the range of g(x)?
-Jil~•f-
Q hich one of the following is NOT an odd
unction.
(A) f(x) - 1
~:n;J-r~ ~ (,5 / €) (B) f(x + 1) - 1
(C) f (x - l) - 1
2• (.-l J ~) = l - ' I O Jt3 @tcx-1) +1
14. Let g(
= (:-3, ,~
e u ct ion whose graph is the image of the graph off (x) after the following
transformations in the following order: a vertical dilation by a factor off .follo:,.xed by a horizontal
translation by -1 units followed by a reflection over the y-axis.Jl.,<J=2 ~>t+ I I
a. g(x) may be expressed as g(x) = af(b(x + c)). Find the values of a, b, and c.
A -: 1 b:: .. l £= ... f
b.
l 2 11-,c 2, , DJ-> r, f -, t tr
f
The point (2,9) is on,,~e gr,a_ph,of cl)~ corresponding point on the graph of g(x).
c. Below ~re select values of the function x . Find the value of g( 4).
X -3 -2 -1 0 1 2 3 4
f(x) -36 5 24 27 20 9 0 -1
2i (-'t ... }
2-ff--3)
'2 .,,) ::._a
CBHS AP Precalculus 2025/26 - Periodic Graphs, Test Review (Day 12)
Test Review: Periodic Functions
The test will be no calculator, so for the best practice, complete this review without the aid of a calcul?t-:!: _
Desmos.
3,/L - 2 x'- I ::: o-1,iJ\-:: .!, s )
1
*
1. Select all that are solutions to the following equation. .Vl )(.~J.J
(x-, ..3 :::1!:.r.uc.-l
eoe= TT-~( .1. \ )
2
3 tan 0 - 2 tan 0 - 1 = o x- 1 _ , " J2 s
- - - - - -J - ~ ·--- f7-4'c:Aatt ( °i
: arctan(½)
TC - arctan (½)
5 ;,,2. + , ~ .:.. .i r. 6 - (- o•
~o.n 1.-+- \ ::: tec.1- J(l--co~')tl + .1l'o'S :
2.
1.,. to-t:'I.::: c:..sc'2- 3 -3Gof"'8 +5"to5S-( -o
serecr dll that are solutipps to the following equation.
<o, -.n -l fi" noel l\a➔ 1. 2 + cos 0 - o
sm 0 -
. 1 -
3
5
arccos(2) {rr-- arccos (i)) 2TC - arccos (½) 1
2TC + arccos (½)
TC - arccos(2) arccos (½) 2TC - ar;cos(2) ___: eOS (½[I •
Use the below table of f(x), graph of g(x), and equation of h(x) to answer #3-9
4
3 X -3 -2 -1 0 1 2 3
f(x) 2 1 3 0 -3 -2 -1
2
-
2 3 4
-1 h(x) = 3x - 6
-2
-3
-4
4. Find f- 1 (-3)
.L
9. Find on expression for h- 1 (x)
'd::. 3x - b
f:zjy
CBHS AP Precalculus 2025/26 - Periodic Graphs, Test Review (Day 12)
, (x) be the periodic function tor which y = f (x) is graphed below. Use this question to answer #10-13.
5
4,
3
2
I
.. 2 -1 oI 3 5
-3
10. What is the period off (x)?
2-
11. What is the amplitude off (x)?
lf r
-5
or,;i" r.:JMM~
12. Let g(x) = 2f(x - 1) + 3.
What is the range of g(x)?
-Jil~•f-
Q hich one of the following is NOT an odd
unction.
(A) f(x) - 1
~:n;J-r~ ~ (,5 / €) (B) f(x + 1) - 1
(C) f (x - l) - 1
2• (.-l J ~) = l - ' I O Jt3 @tcx-1) +1
14. Let g(
= (:-3, ,~
e u ct ion whose graph is the image of the graph off (x) after the following
transformations in the following order: a vertical dilation by a factor off .follo:,.xed by a horizontal
translation by -1 units followed by a reflection over the y-axis.Jl.,<J=2 ~>t+ I I
a. g(x) may be expressed as g(x) = af(b(x + c)). Find the values of a, b, and c.
A -: 1 b:: .. l £= ... f
b.
l 2 11-,c 2, , DJ-> r, f -, t tr
f
The point (2,9) is on,,~e gr,a_ph,of cl)~ corresponding point on the graph of g(x).
c. Below ~re select values of the function x . Find the value of g( 4).
X -3 -2 -1 0 1 2 3 4
f(x) -36 5 24 27 20 9 0 -1
2i (-'t ... }
2-ff--3)
'2 .,,) ::._a
CBHS AP Precalculus 2025/26 - Periodic Graphs, Test Review (Day 12)
