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