Types of Functions - Grade 11
Straight Line y = ax+q, y = mx+c
M = gradient
- parellel: m1=m2
- perpendicular: m1 x m2 = -1
- no gradient: straight horizontal line
- undefined gradient: straight vertical line
q = y-intercept
m less than 0 = decreasing, more than 0 = increasing
Hyperbola y = (a/x-p) + q
a: shape
- a more than 0: 1st + 3rd Quad,
- a less than 0: 2nd+4th Quad
q: vertical asymptote (x=)
p: horizontal asymptote (y=)
Axis of Symmetry: y=mx+c and y=-mx+c (m=1)
- sub in co-ordinates to find c
Parabola y= ax^2 + q
(Quadratic) - a: less than 0 = sad NB: converting
- a: more than 0 = happy between formulas
- q: y-intercept
y= a(x-p)^2 + q (TP Form)
x = -b/2a
- p: axis of symmetry + X@TP
= (x1+x2)/2
- NB: sign change = x-value at TP
- q: max/min value + Y@TP
y= a(x-x1)(x-x2)
- x1 and x2 = x-intercepts
- x = x-value at TP
Exponential y= b^x +q OR y= a(b^x-p) + q
b: shape
- b>1: increasing or decreasing RHS
- 0<b<1: Increasing or decreasing LHS
q: horizontal asymptote (y=)
- +q = above asymptote
- (-q) = below asymptote
a: down or up
- (a) = up
- (-a) = down
Straight Line y = ax+q, y = mx+c
M = gradient
- parellel: m1=m2
- perpendicular: m1 x m2 = -1
- no gradient: straight horizontal line
- undefined gradient: straight vertical line
q = y-intercept
m less than 0 = decreasing, more than 0 = increasing
Hyperbola y = (a/x-p) + q
a: shape
- a more than 0: 1st + 3rd Quad,
- a less than 0: 2nd+4th Quad
q: vertical asymptote (x=)
p: horizontal asymptote (y=)
Axis of Symmetry: y=mx+c and y=-mx+c (m=1)
- sub in co-ordinates to find c
Parabola y= ax^2 + q
(Quadratic) - a: less than 0 = sad NB: converting
- a: more than 0 = happy between formulas
- q: y-intercept
y= a(x-p)^2 + q (TP Form)
x = -b/2a
- p: axis of symmetry + X@TP
= (x1+x2)/2
- NB: sign change = x-value at TP
- q: max/min value + Y@TP
y= a(x-x1)(x-x2)
- x1 and x2 = x-intercepts
- x = x-value at TP
Exponential y= b^x +q OR y= a(b^x-p) + q
b: shape
- b>1: increasing or decreasing RHS
- 0<b<1: Increasing or decreasing LHS
q: horizontal asymptote (y=)
- +q = above asymptote
- (-q) = below asymptote
a: down or up
- (a) = up
- (-a) = down
