Algebra Final by maryfutbol

csc x = 1/sin x
sec x = 1/cos x
cot x = 1/tan x

sin (x/2) = radical((1 - cos x) /2)
cos (x/2) = radical((1 + cos x) / 2)
tan (x/2) = (sin x / 1 + cos x)

Transl­ations

g(x) = f(x) + k is the graph of f(x) translated k units up when k > 0 and k units down when k < 0.

g(x) = f(x − h) is the graph of f(x) translated h units right when h > 0 and h units left when h < 0.


Reflec­tions

g(x) = -f(x) is the graph of f(x) reflected in the x-axis.
g(x) = f(-x) is the graph of f(x) reflected in the y-axis.

Dilations

g(x) = a · f(x) is the graph of f(x) expanded vertically if a > 1 and compressed vertically if 0 < a < 1.

g(x) = f(ax) is the graph of f(x) compressed horizo­ntally if a > 1 and expanded horizo­ntally if 0 < a < 1.

Domain: The domain of a function is the set of all possible input values (often the "­x" variable), which produce a valid output from a particular function. It is the set of all real numbers for which a function is mathem­ati­cally defined.

Range: The range is the set of all possible output values (usually the variable y, or sometimes expressed as f(x)), which result from using a particular function.

tan x = sinx/cosx
cot x = cosx/sinx

cos2x = cos²x - sin²x
sin2x = (2sinx­)(cosx)
tan2x = (2tanx / 1 - tan²x)

constant function
f(x) = a graph is a horizontal line

identity function
f(x) = x points on graph have coordi­nates (a, a)

quadratic function
f(x) = x² graph is U-shaped

cubic function
f(x) = x³ graph is symmetric about the origin

square root function
f(x) = sqrt(x) graph is in first quadrant

reciprocal function
f(x) = 1/x graph has two branches

absolute value function
f(x) = │x│ graph is V-shaped

sin²x + cos²x = 1
tan²x + 1 = sec²x
1 + cot²x = csc²x

Logari­thmic
y = ln x

Expone­ntial
y = b^x