Function Notation
If f(x) = 2x - 1
Find f(3)
7
Given the first four terms of a geometric sequence -4, -8, -16, -32,...
Write the Recursive Formula.
an = 2(an-1)
In a laboratory experiment, a certain type of bacteria reproduces every day. On day 1, there are 3 bacteria present. By day 2, the population has increased to 6 bacteria; by day 3, there are 12 bacteria; and this doubling continues each day.
How many bacteria will there be on the 15th day?
49,152 bacteria
Given the function f(x) = 3(2)x
Find the asymptote.
y = 0
Given the function f(x) = 3x
Find the y-intercept.
(0, 1)
f(x)=2(3)x-1+3 and g(x)=(1/2)x
Find f(1) - g(-1)
3
Given the first three terms of a geometric sequence 3, -9, 27,... Write the Explicit Formula.
an = 3(-3)n-1
In a greenhouse, a specific plant species is being studied. The number of plants starts at 5 on day 1. By day 2, the number of plants has tripled to 15; on day 3, it increases to 45, and this tripling continues each day.
How many plants will there be on the 12th day?
885,735 plants
Given the function f(x) = 6(0.4)x + 4
Find the asymptote.
y = 4
Given two terms of a geometric sequence
a2 = 8 and a3 = 16
Find a1
a1 = 4
DAILY DOUBLE
If f(x)=5x+2 and g(x)=3(2)x-1+2
Find f(0) + 2g(1)
25+2(5) = 35
A geometric sequence has the following features:
a1 = -8 and r = 0.5
Write the explicit formula for the sequence.
an = -8(0.5)n-1
DAILY DOUBLE
A scientist is studying a particular radioactive substance. The initial amount of the substance is 100 grams. Every day, the substance decays by half of its current amount.
How much of the substance will be left after 6 days?
1.5625 grams
Given the function f(x) = 4x - 2
Find the Domain.
(-infinity, infinity)
What is Coach Lord's birthday (month and day)
October 26
Given the following points from the table of a function f: (-1, 0), (0, 1), (1, 4), (2, 9), find x when f(x)=0.
A geometric sequence has the following features:
a3 = 12 and r = 2
Write the explicit formula for the sequence.
an = 3(2)n-1
A local library starts with 50 new books. Each month, the library acquires 4 times as many new books as it did the previous month.
How many new books will the library have acquired after 6 months?
Total=50+200+800+3200+12800+51200=68650
Given the function f(x) = 3(2)x + 6
Find the Range.
(6, infinity)
Coach Lord has two dogs, Kala and Kosmo. Kala is a rottweiler. What breed is Kosmo?
Lab
f(x) = 3x and g(x) = 2(4)x-1+1
Find f(2) - g(1)
9 - 3 = 6
an = 4(5)n-1 is the explicit formula for a geometric sequence.
Write the recursive formula for the same sequence.
an = 5(an-1)
A car rental company has a fleet of 80 cars at the beginning of the year. By the end of the first year, the company has 120 cars. At the end of the second year, the fleet has grown to 180 cars.
Assuming the number of cars grows geometrically each year, find the common ratio of growth.
r = 1.5 or 3/2
Given the function f(x) = 2(4/3)x-1 - 5
Is it exponential growth or decay?
Growth
Which former president's image appears on the $50 bill?
Ulysses S. Grant