Graphing Problems
What is the RANGE of:
f(x)=log2(x+5)-1
Range= All real numbers
log6(36)=?
2
Kieran and Bube are working on solving the following problem:
log5(25x-(1/5))=5
Here are the steps they took:
55=25x-(1/5)
55+(1/5)=25x
55/25+(1/5)/25=x
If told that their answer can be left as a fraction, will they receive full credit for this problem?
Yes. Their answer is correct.
In 2010 a new pair of headphones cost $9.00. The price increased by 14% each year. Write an exponential growth function to represent this situation.
Name the following Property
am*an=am+n
Product Rule/Property
What is the DOMAIN of
f(x)=log2(x+5)-1
(-5, infinity)
63*63=?
69=10,077,696
Randy submitted the following
53x-4=25
log5(53x-4)=log5(25)
3x-4=5
x=3
What was his error? What should the correct answer be?
log5(25)=2
x=2
Your car cost $15,000 when you purchased it in 2022. The value of the car depreciates by 15% annually. How much will your car be worth in 2031?
$3474.25
Complete the following Property
am/n=?
(am)1/n
Identify 2 points on the graph of
f(x)=-(1/3)x-1+4
(1,3)
(0,7)
etc.
log(100)+log(1000)=?
5
The growth rate of a bacterial culture is 150% each hour. Initially, there are 10 bacteria. Describe and correct the error in finding the number of bacteria in the culture after 8 hours.
b(t)=10(1.5)t
b(8)=10(1.5)8=256.3
After 8 hours, there are about 256 bacteria in the culture.
The formula is b(t)=10(1+1.5)t
The correct answer is 15258.79 bacteria.
y=(120,000)e.015t
Determine the following:
Initial Value
Rate
Kind of Function
I:120,000
R:15%
F: Compound continuous function
logb(b)=?
logb(1)=?
1, 0
Where is the asymptote of the following
f(x)=3e-x-3
Asymptote at y=0
log7(49)+log8(4096)-ln(7.389)
4
In 2010 I purchased a car for 25,000. The value of the car decreases by 14% annually. Describe and correct the error in finding the value of the car in 2015.
v(t)=25,000(1.14)t
v(5)=25,000(1.14)5=48,000
Depreciates=(1-r)
v(t)=25,000(.86)t
v(5)=25,000(.86)5=11760.68
For college you take out a loan with 5.8% interest compounded yearly. The amount of the loan was $40,000. If you wanted to pay off the loan in 13 years, how much should you pay each month?
$533.64 a month.
Complete the following
logb(x)-logb(y)=?
logb(x/y)
What is the end behavior of
f(x)=log(1/2)(x+4)
As x approaches 0, f(x) approaches infinity
As x approaches infinity, f(x) approaches negative infinity.
(53-2)ln1
Answer=11
What errors were made? What is the correct answer?
Variety of mistakes could have been made.
You apply for a credit card with 2.75% interest rate, compounded monthly. You make an initial purchase of $300. How much will you pay because of interest after a year?
$8.35
Simplify the following
log3((x/9)5)
5log3(x)-10