Unit 2 Flashcards
(17 cards)
What is the general form for finding the nth term of an arithmetic sequence when you know a0 or ak?
an=a0+dn
an=ak+d(n-k)
What is the general form for finding the nth term of a geometric sequence when you know g0 or gk?
gn=g0(r)^n
gn=gk(r)^n-k
What is the general form of a linear function?
f(x)=mx+b
What is the general form of an exponential function?
f(x)=a(b)^x
State the negative exponent property for exponents
b^n-1=1/b^n
State the rational exponent property
b^1/k=ksqrtb
What is the natural base?
e, which is approx 2.71828…
log(base e)= lnx
The difference between the predicted and actual values in a model is called what?
the error
Write a mathematical equation that represents the statement, “The composition of a function f, and its inverse function, g, is the identity function”
f(g(x))= g(f(x)) = x
Explain how to convert between exponential and logarithmic form
if b^p = N then, log (base b)N = p where b>0 and b does not equal 1
Evaluate the following
- lne
- log (base b)b
-e^0
b^0
- lne =1
- log (base b)b= 1
- e^0= 1
- b^0= 1
When the y-axis is logarithmically scaled, data of functions that demonstrate exponential characteristics will appear….
linear
given a table of values, when input values are proportional over equal-length output-value intervals, the function type is…
logarithmic
Sketch a graph that is increasing at an increasing rate
the right side of a concave up graph
Sketch a graph that is decreasing at a increasing rate
the right side of a concave down graph
Sketch a graph that is decreasing at a decreasing rate
the left side of a concave up graph
Sketch a graph that is increasing at a decreasing rate
the left side of a concave down graph
