Page 2 Memorization Quiz Flashcards
(26 cards)
What type of growth does an arithmetic sequence exhibit?
An arithmetic sequence grows linearly.
What is the general form of an arithmetic sequence?
An = a₁ + (n-1)d
What is the definition of common difference?
The difference between consecutive terms.
What type of growth does a geometric sequence exhibit?
A geometric sequence grows exponentially.
What is the general form of a geometric sequence?
aₙ = a₁ (r)ⁿ⁻¹
What is the definition of common ratio?
The constant proportional change between terms.
What is the general equation of a linear function in point-slope form?
y - y₁ = m (x - x₁)
What is the general equation of an exponential function?
y = a • b^x
What characterizes the common ratio of exponential growth functions?
They have a common ratio that is greater than 1.
What characterizes the common ratio of exponential decay functions?
They have a common ratio that is between 0 and 1.
a^x * a^y =
a^(x+y)
a^x / a^y = a
a^(x-y)
(a^x)^y =
a^(xy)
a^x•b^x =
ab^x
a^(-x) =
1/(a^x)
What does F(g(x)) mean?
Substitute g(x) into f(x)
What is the result of composing a function with its inverse?
It results in X
f(f⁻¹(x)) = x
f⁻¹(f(x)) = x
How do you algebraically find the inverse of a function?
By swapping x and y, then solving for y.
The inverse of a function is a reflection over
It is a reflection over the line y = x.
What happens to the domains and ranges of inverse functions?
They are swapped.
How can the equation aᶜ = b be rewritten as a logarithm?
logₐb = c
log_a(xy) =
log_a(x) + log_a(y)
log_a(x/y) =
log_a(x/y) = log_a(x) - log_a(y)
log_a(x^y) =
log_a(x^y) = y * log_a(x)
