AP Precalculus Flash Cards

a positive residual indicates that the predicted value is an

underestimate

a negative residual indicates that the predicted value is an

overestimate

explicit rule for the nth term of a geometric sequence given common ratio r, and the ak term

an = ak x r^n-k

explicit rule for the nth term of an arithmetic sequence given common difference d, and the ak term

an = ak + d(n-k)

residual

actual value - predicted value

a model is considered appropriate for a data set if the residual plot

appears without pattern

error (in a model

predicted value - actual value

f and g are inverse functions if

f(g(x)) = g(f(x)) = x

if the y axis is logarithmically scaled

equal-sized increments on the y-axis represent proportional changes in the output variable

in a semi-log plot where the y-axis is logarithmically scaled, exponential functions will appear

linear

key features of y = sinx

domain: all real numbers, range: [-1, 1], period: 2π, amplitude: 1, midline: y=0, passes through (0,0)

key features of y = cosx

domain: all real numbers, range: [-1, 1], period: 2π, amplitude: 1, midline: y=0, passes through (0,1)

horizontal translation c units to the right if c > 0, or, c units to the left if c < 0

f (x - c)

vertical translation c units up if c > 0, or, c units down if c < 0

f (x) + c