AP pre-calc

Arithmetic sequence

a_n=a_k+d(n-k)

A linear function

f(x)= y₁+m( x - x₁ )

Geometric sequence

g_n = g_kr^(n-k)

G Exponential Function

f(x) = y₁r^(x-x₁)

b^(1/k)

square root k

if a quantity doubles every day d, then f(d) = (2)^d gives the quantity after d days.

An equivalent form f(d) = (2⁷)^d/7

Exponential function

over equal length input-value intervals the outputs are proportional

Logarithmic functions

over equal-length output value intervals the inputs are proportional.

y-axis is logarithmically scaled exponential data or functions appear…

linear

when the graph is decreasing, concave up then…

then the rate of change is negative, increasing at an increasing rate

when the graph of f is increasing and concave up then…

the rate of change is positive and increasing at an increasing rate

if the graph of f is increasing and concave down then…

the rate of change is positive, decreasing at a decreasing rate

if the graph of k is decreasing and concave down then…

the rate of change is negative, decreasing at a decreasing rate

if the difference in outputs are increasing the function is…

concave up

if the difference in outputs are decreasing the function is concave…

down