Precalc Test 1

y=f(x)+c

vertical shift upward by factor of c

y=f(x)-c

vertical shift downward by factor of c

y=f(x+c)

horizontal shift left by factor of c

y=f(x-c)

horizontal shift right by factor of c

y=-f(x)

reflects the graph across the x-axis

y=f(-x)

reflects the graph across the y-axis

y=c(f(x)), when c>1

vertical stretch by factor of c

y=c(f(x)), when 0<c<1

vertical shrink by a factor of c

y=f(cx) when c>1

horizontally shrinks by a factor of c

y=f(cx) when 0<c<1

horizontally strectches by a factor of c

domain

all possible values of x

range

all possible values of y

slope of parallell functions

(m1)=(m2)

slope of perpendicular functions

(m2)=-1/(m1)

how to eliminate an imaginary denominator

multiply by the reciporical. (X + Xi) x (X - Xi)

how to find an inverse

swap y and x, then solve for “x”

d= -/ ((x₂)-(x₁))² + ((y₂) - (y₁))²

distance formula

((x₁+x₂)/2) , ((y₁+y₂)/2))

midpoint formula

r²=(x-h)²+(y-k)²

circle standard formula

(x²+y²+Dx+Ey+F=0)

general form of circle

a number in the domain (x) corresponds to at least 2 in the range (y)

NOT a function, due to repeating x values

(f(x+h)-f(x))/h

difference quotient formula

y-y₁=m(x-x₁)

point slope form

y=mx+b

slope intercept form

Ax+By+C=0

general form

how to graph general form?

let y=0 to get an x-int, then x=0 for a y-int, and connect w/ straightedge.