Story Time
f(g(x))
f(x)= vs x=___
Arithmetic/Geometric Sequences
Explicit/Recursive Formula
100

At a sushi restaurant, each sushi costs $5 and drinks cost $2 each. You begin with a drink and 1 sushi.

Write a function that demonstrates the relationship between number of sushi and cost of your meal.


C(s)=5s + 2

100

f(g(2))

g(x)=x+2        f(x)=3x

f(g(2))=12

100

What is the difference between solving for f(x) when given x and solving for x when given f(x)?

One is giving you the variable and asking for the functions total value.

The other is giving you the functions total value and asking you to solve for the variable that gave that total.

100
Is this sequence Arithmetic, Geometric, or Neither? 2, 6, 18, 54, 162
Geometric
100

What is the first term of this Explicit Equation? t(n) = 2n + 3

5

200

You and 4 friends agreed to meet at the movies. To save time, the first friend to arrive offered to buy everyone's ticket snacks and be reimbursed later.

The total cost was $100. How much does each person owe you?

20

200

f(g(-2))

f(x)=x+5        g(x)= -3x

f(g(-2))= -9

200

Solve for f(x) given x=3

f(x)=2x-5

f(x)=1

200
Is this sequence Arithmetic, Geometric, or Neither? 1, 5, 6, 9, 10
Neither
200

What are the first four terms of this Explicit Equation? t(n) = 4n + 1

5, 9, 13, 17

300

At Honey Beepot, the bulk price for honey is $2.50 per pound, with a minimum purchase of 20 pounds. If Bobby paid $80 for some honey, by how many pounds did Bobby's purchase exceed the minimum?

12

300

f(g(1/2))

f(x)=1/4 + x       g(x)=(1/2)x

f(g(1/2))=1/2

300

Solve for x when given f(x)=13

f(x) = 2x + 9

13 = 2x+9

x = 2

300
Is this sequence Arithmetic, Geometric, or Neither? 3, 5, 7, 9, 11
Arithmetic
300
What is the difference between the Explicit Formula and the Recursive formula?
Explicit: substitute in the number of each term (1 for 1, 2 for 2, etc) Recursive: substitute in the term before
400

At a craft fair, Tony bought 3 items, Isabella bought 1 item, and Tanisha bought 5 times as many items as Tony and Isabella did combined. Which of the following represents the number of items Tanisha bought?

(3+1)*5

400

f(g(-3))

f(x) = -2x2     g(x) = 3x+4

f(g(x))=-50

400

Solve for f(x) when given x=5

f(x) = 3x + 6(x-2)

f(x) = 33

400
What is the common difference? 4, 8, 12, 16, 20
4
400

What is the second term of this Recursive Sequence? t(1) = 2; t(n) = t(n-1) + 2

4

500

Tina has tracked her quiz scores and noted that each hour of studying added 15% (*1.15) to her weekly quiz grade.

Her first quiz grade was 62%. What do you predict her next quiz score will be if she studies 4 hours that week?

94%

500

f(g(3))

f(x)= 5x              g(x) = (1/3)x

f(g(x)) = 5

500

Solve for x when given f(x)= 34

f(x)=2x2+2

x = 4

34=2*x2+2

500
What is the common ratio? 4, 8, 16, 32, 64
2
500

What are the first four terms of this Recursive Sequence? t(1) = 0; t(n) = t(n-1) - 4

0, -4, -8, -12

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