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vertical line test
function cannot cross a vertical line more than once TERM 2
U
DEFINITION 2 union sign means set is togetherex: 1/x graph the domain would have a U because small gap where not continuous but set still together TERM 3
e^
DEFINITION 3 =1anything to the zero power becomes one TERM 4
Definition of a derivative
DEFINITION 4 the derivative of f(x) with respect to x is the function f^t (x) defined as rise/run <--> f^t (x) = f (x+h) - f(x)/ h TERM 5
Brackets
DEFINITION 5 use them when there is a pointex: greater than or equal toLess than or greater than would use ( )
Limits
is finding where a function is heading"as i approach x from the (left - or right + ) my y values are..." TERM 7
linear equation
DEFINITION 7 y = mx +bm is slope TERM 8
maximum
DEFINITION 8 highest value graph actually hits TERM 9
minimum
DEFINITION 9 lowest value graph actually hits TERM 10
Trig functions
DEFINITION 10 sin(theta) = y/rcos(theta) = x/rtan(theta = y/x
continuous definition
f(x) is continuous at x=a if the lim f(x) = f(a) x->a TERM 17
Theorem 1.5.
DEFINITION 17 a) a polynomial is continuous everywhereb) a rational function is continuous at every point where the denominator is not zero, and is discontinuous where the points at the denominator equal zero TERM 18
how to do
limits
DEFINITION 18
- check domain by plugging in number. is it continuous?2) can you factor or reduce to make continuous?3) if not draw the graphnote: lim v. lim v. lim x-> 3+ x-> 3- x->3are all different depending on the graph, and tell you if the graph is going towards negative infinity positive infinity, both by plugging in numbers, or 0 TERM 19
graph 18 sinx/x
DEFINITION 19 = 1 TERM 20
x/x
DEFINITION 20 when limit heading to infinity x/x =1 when x not equal to zero lim x-> infinity
Power rule
d/dx ( x^n ) = n * x^n -1put exponent in front, subtract one from exponent TERM 22
Derivative of a graph
DEFINITION 22 is the slope of the tangent line TERM 23
Product rule
DEFINITION 23 d/dx( f * g)^1 = f(x) g1(x) + f1(x) g(x)note: product rule is used to find the derivatives if it is a product (being multiplied)always find f prime and g prime first TERM 24
second derivative
DEFINITION 24 is a derivative of the first derivative (so take a derivative of whole thing, then take a derivative of what you took a derivative of) TERM 25
Definition of derivatives
DEFINITION 25 f^1 (a) = lim f(x)- f(a)/ x-a x->a = lim f(a+h) - f(a)/h n->0 = m tan (slope of a tangent line)
chain rule derivative of a
composition
used when there is a composition (something multiplied by something else) y^1 = f^1 (g(x)) * g^1(x)translatedy^1 = (derivative of the outside function) multiplied by the (derivative of inside function)
