Exponential and Logarithmic Functions Flashcards
What is the parental function for exponential decay functions?
0 < b < 1
What letter in ab^(x-h)+k represents a left/right slide (horizontal change)?
h
What letter in ab^(x-h)+k represents an up/down slide (vertical change)?
k
What is the parental function for exponential growth functions?
f(x) = b^x, if b > 1
What function is used to model exponential growth/decay functions?
A(t) = a(1 + r)^t
A(t) = a(1 + r)^t: what does A(t) stand for?
Amount after t time periods.
A(t) = a(1 + r)^t: what does a stand for?
Initial amount
A(t) = a(1 + r)^t: what does r stand for?
Rate of growth (r > 1) or decay (r < 1)
A(t) = a(1 + r)^t: what changes depending on if it is growth or decay?
+/-
A(t) = a(1 + r)^t: what does t stand for?
Number of time periods
What does the equation y = ax represent?
Direct variation
In y=ax what is the nonzero constant?
Constant of variation
What is another name for the constant of variation?
Coefficient of variation
What does the equation y = a/x represent (a ≠ 0)?
Inverse variation
What do you write when there is no variation?
Neither
Multiplying x by y will determine what?
If they are the same, it is inverse.
When one quantity varies with respect to two or more quantities?
Combined variation
When one quantity varies directly with two or more quantities?
Joint variation
If it doesn’t say, it is
direct (for joint variation).gmmjtty
What is letter that represents the constant of variation?
K
If 10^x = a, then x =
Log10a
Or
Log a
To find an inverse,
Switch x and y
And then rearrange
To graph an inverse,
Reflect over line y=x
What are characteristics of log graphs?
Vertical asymptote
Range of ARNs
What numbers can’t you take a log of?
Negative
What does the ERROR message usually signify?
The asymptote
What type/how many asymptote a does a log graph have?
1 vertical asymptote
To find the x-intercept, plug in _ for _.
0 for y
