PRACTICE
Consider the function “machines” provided. Arrange all four machines in the proper order
to satisfy the conditions below.
(1) Input 6 into the first machine; 11 is the output from the last machine
CORRECT ORDER OF MACHINES:
___________
___________
___________
___________
(BONUS) Input 64 into the first machine; 131,065 is the output from the last machine
CORRECT ORDER OF MACHINES:
___________
___________
___________
___________
Again, consider the function machines. Arrange all four machines in the proper order
to satisfy the conditions below.
CHALLENGE
(2) Input 3 into the first machine; —1/2 is the output from the last machine
CORRECT ORDER OF MACHINES:
___________
___________
___________
___________
(3) Input —4 into the first machine; —49 is the output from the last machine
CORRECT ORDER OF MACHINES:
PRACTICE
___________
___________
___________
___________
Consider the functions 𝑓(𝑥) = 4𝑥 + 3 and 𝑔(𝑥) = 5𝑥. Perform each operation.
(4) 𝑓(5) _________
(5) 𝑔(−3) _________
(6) 𝑓
(7) 𝑔 𝑓(−1)
(8) 𝑓 𝑔(2)
(9) If 𝑓(𝑥) = 15,
what was x? _______
PRACTICE
_________
_________
_________
Consider the functions 𝑓(𝑥) = 𝑥 − 3 and 𝑔(𝑥) = −𝑥. Perform each operation.
(10) 𝑔(−8) _________
(11) 𝑓(10) _________
(12) 𝑓(1) _________
(13) 𝑓 𝑔(22)
(14) 𝑔 𝑓(−2)
(15) 𝑔 𝑔(−4)
_________
(16) If 𝑓(𝑥) = 6,
what was x? ________
_________
(17) If 𝑔(𝑥) = 25,
what was x? ________
_________
(18) If 𝑔 𝑓(𝑥) = 1,
what was x?
______
REVIEW
Evaluate each expression using the correct order of operations (PEMDAS).
(19) 30 − [(33 ÷ 11)(6 − 6)] _________
(20) 29 − 9 ∙ 2 + 6 ∙ 3 _________
(21) −1(10 − 6)
(22) 15 − 2(6 − 4) _________
REVIEW
_________
(23) Which of the following expressions is not equal to 4?
a) 80 ÷ 10 − 2(11 − 13)
REVIEW
b) √144 − 4(4 − 7 ∙ 2)
c)
(5 + 1) − (13 − 3)
d) 3 + 2 ∙ 5 − 3
(24) Which of the following expressions is equivalent to 𝑥 − 2𝑥 − 24 ?
a) (𝑥 + 6)(𝑥 − 4)
b) (𝑥 + 3)(𝑥 − 5)
c) (𝑥 − 12)(𝑥 + 2)
d) (𝑥 − 6)(𝑥 + 4)
REVIEW
(25) In the space at
right, show that your answer to
#24 is equivalent to 𝑥 − 2𝑥 − 24.
REVIEW
Using the factors in the answer bank at right, write each expression
in factored form. Some factors may be used more than once.
(26) 9𝑥 − 1
(
(3𝑥 − 1)
(27) 𝑥 + 3𝑥 + 2
)(
)
(
ANSWER BANK:
)(
)
(3𝑥 + 1)
(𝑥 + 2)
(28) 𝑥 − 2𝑥 − 8
(
REVIEW
)(
(𝑥 − 4)
(29) 3𝑥 − 13𝑥 + 4
)
(
)(
)
(𝑥 + 1)
Solve each equation.
(30) 6𝑥 − 3𝑥 + 2 = −10 _________
(31) 5𝑥 + 2 = −𝑥 + 14 _________
(32) −4(𝑥 + 2) = 3(𝑥 + 2) _________
(33) 2𝑥 + 3(𝑥 + 5) = 0 _________
(34) 𝑥 − 25 = 0 _______ _______
(35) 𝑥 + 5𝑥 − 14 = 0 _______ _______
REVIEW
(36) Which equation does not have a solution of 3?
a) −4𝑥 + 1 = −11
b) 3𝑥 + 7𝑥 = 30
c) 2(𝑥 + 1) = 7
d) 𝑥 − 9 = 0