calc exam

point slope form

y-y1 = m(x-x1)

slope intercept form

y=mx+b

how to find slope

m = (y1-y2) / (x1-x2)

when you multiply or divide by a negative in an inequality, you should

switch the sign to face the other direction

base change formula

ln (x) / ln (b)

exponential function form

y = a • b^x

average rate of change means

slope

in an exponential function, b is equal to

b= 1+r, where r is the growth or decay rate in decimal form

definition of log

log b (x) = y , b^y = x

how to find the inverse of a function

switch x and y and solve for y, you may need to factor if there is a fraction

graphs of log functions

horizontal asymptote at y=0 adjusts with transformations. Base log of log = 1.

graph of exponential

vertical asymptote at x=0, adjust with transformations

inside the function transformations affect the

y-axis. f(-x) means reflect over the y-axis, f(x+h) makes it move left or right, and f(9x) horizontally compresses it bringing it closer/further from the y-axis

transformations outside of the function affect

the x-axis. f(x) + 9 makes it go up or down, 9f(x) vertically compresses it moving it closer/further from the x-axis, and -f(x) reflects it over the x-axis.

quadratic function standard form

y = ax² + bx + c

quadratic function vertex form

y = a (x-h) +k

how to go from one quadratic form to another (standard, vertex)

for vertex to standard, just multiply out
for standard to vertex a = a , h = (-b/2a) k = f(h)

factoring steps and types

1. look for GCF

2. Identify type of factoring. Quadratic find c factors = b, Ac find ac factors = b.

quadratic function graph

u shaped curve that either opens up or down depending on if a is pos or negative