graphs to know

Basic Parabolas (x² + #) and lines

1 1

2 4

Complex parabolas

1 1

2 4

cubic x³

sideways backwards s (starts bottom left to top right)

Absolute value |x|

V

reciprocal 1/x

Top right and bottom left

Exponential e^x

tip to memorize: exponent means up (goes up and starts left of x axis) (not below x axis) (goes more up than right) (u shape)

ln x

Starts from bottom right (below x axis) to top right (above axis) (goes more right than up) (c shape)

\sqrt{x}

Like ln x but starts from (0,0) (c shape) (goes more right than up)

sin x

hill / hump / upside down u starts from zero to pi

parabola/ u shape from zero to pi (continue to the right) (connected like a squiggle)

(period: 2pi)

(X axis is in the middle of all humps)

cos x

Y axis in the middle of hump

hill / hump / upside down u starts from negative pi/2 to pi/2

parabola/ u shape from pi/2 to 3pi/2

(continue to the right) (connected like a squiggle)

(period: 2pi)

(X axis is in the middle of all humps)

csc x

Parabola u shape from zero to pi

Upsidedown parabola from pi to 2pi

parabolas and upside down parabolas separated by vertical asymptotes (dashed lines)

period: 2pi

sec x

Y axis in the middle of Parabola u shape

Upsidedown parabola from pi/2 to 3pi/2

parabolas and upside down parabolas separated by vertical asymptotes (dashed lines)

period: 2pi

tan x

y axis in middle

sideways backwards s (going from bottom left to the top right) (goes up)

starts from negative pi/2 to pi/2 and repeats from pi/2 to 3pi/2 (separated with dashed lines (vertical asymptotes))

cot x

sideways normal s

Starts from top left to bottom right (goes down)

From zero to pi and pi to 2pi (separated by dashed lines (vertical asymptotes))

Isosceles and Equilateral Triangles