Functions
Which of the following is NOT a function?
A) y=x+2
B) x=y^2
C) f(x)=3x−1
D) (1,2),(2,4),(3,6)
B) x=y^2
A sequence is: 5, 9, 13, 17, …
Without finding many terms, explain how you know it is arithmetic.
Because the difference between consecutive terms is constant (+4).
Simplify: x^3⋅x^4
x^7
what is the value of log10^1000?
3
What does the formula>> sin^a+cos^2a equal to?
1
Explain why a vertical line crossing a graph twice means it is not a function.
One x-value has multiple y-values, violating the definition of a function.
A sequence has first term 12 and common difference -4. Predict what happens to the terms over time.
The sequence decreases continuously because each term becomes 4 smaller.
3^(x+1)=81
3
What is log(−5)?
This logarithm is undefined because its argument is negative.
What is the formula allows you to find cos^2a if you only know tan^2a?
1/1+tan^2a
Find the domain of f(x)=1/(x-5).
All real numbers except x = 5
Two students disagree:
Student A: “Every arithmetic sequence grows forever.”
Student B: “Some arithmetic sequences decrease.”
Who is correct? Explain
Student B is correct. Arithmetic sequences can increase or decrease depending on the common difference. Negative difference → decreasing.
A population doubles every year. What is the growth factor?
2
What is log_a^(b/c)?
According to the subtraction rule, log_a(b) - log_a(c)
simplify the expression 2sin(15*)cos(15*).
sin(30*)=1/2
A graph starts at (2,-4) and extends upward infinitely. What are the domain and range?
Domain: x≥2
Range: y≥−4
Find the rule for:
10, 15, 20, 25, …
Arithmetic rule:
An=10+5(n−1)
What is the general form of an exponential function?
y=ab^x
What is the rule changes multiplication into addition?
The Product Rule
What is one of the three forms for cos(2a) if cos^2a minus?
sin^2a
A graph is increasing for all x-values. What does this mean?
As x increases, y always increases.
A student says:
“If the difference changes, the sequence must be geometric.”
Why is this false?
Changing differences do not automatically mean geometric. Geometric sequences require a constant ratio. Some sequences are neither arithmetic nor geometric
Why are exponential functions important in real life?
They model population growth, finance, radioactive decay, bacteria growth, technology growth, and many real-world changes.
log(x−3)+log(x+1)=log(2x)
x>3
Unlike other inverse functions, arcctg(-a) can be solved using ..... formula.
pi - arcctg(a)