A Review of Graphing Functions
Cartesian Plane
(2,5)
(-4,3)
(-7,-7)
(1,-3)
What is a function?
x y
y = mx + by = ax2 + bx + c
f(x) = sin xg(x) = ex
f(x) = ln (x+5)
The Vertical Line Test
Linear Functions y = mx + b
slope y-intercept
y = 2x + 3
y = 3x - 4
y = -(1/2)x
Linear Functions
y = 4
x = 2
Quadratic Functionsy = ax2 +bx + c
y = x2
Quadratic Functionsy = x2 - 2x + 1
Quadratic Functionsy = x2 - 2x + 2
y = ax2 + bx + c
+ -or
y = x2
y = -x2
y = ax2 + bx + c
changes width of parabola
y = x2
y = 2x2
y = .5x2
y = ax2 + bx + c
moves parabola up or down
y = x2 + 2x + 1
y = x2 + 2x
y = x2 + 2x - 1
f(x+a)
y = x2 + 2x + 1
y = (x+1)2 + 2(x+1) + 1
f(x+a)
y = x2 + 2x + 1
y = (x+1)2 + 2(x+1) + 1
Graph Transformations
y = ax2 + bx + c
y = ax2 + bx + c
y = (x+h)2 + (x+h) + c
y = ± x2
Free Graphing Calculator Graphing Calculator by Mathlab