Studied by 19 peopleTransformation y = |f(x)|
Negative values of y are reflected in x-axis
Transformation y = f(x) + a
+a in y-axis
Transformation y = f(x + a)
-a in x-axis
Transformation y = af(x)
All y-coordinates ×a
Transformation y = f(ax)
All x-coordinates ÷a
Transformation y = -f(x)
Reflection in x-axis
Transformation y = f(-x)
Reflection in y-axis
When is a binomial expansion valid (yr13)?
For (a + bx)n, valid when | bx/a | < 1
or |x| < a/b
x = an as a log?
n = logax
loga (xk) rearranged
klogax
log(xy)
log(x) + log(y)
log(x/y)
log(x) - log(y)
Order of transformations
x: reflect, stretch, translate | y: translate, stretch, reflect , modulus
π Radians in degrees
180
Condition for increasing function?
dy/dx ≥ 0
Condition for decreasing function?
dy/dx ≤ 0
Condition for local minimum?
d2y/dx2 > 0
Condition for local maximum?
d2y/dx2 < 0
Condition for concave function?
d²y/dx² ≤ 0
Condition for convex function?
d²y/dx² ≥ 0
Percentage Change
Area of circle segment
How to integrate a parametric function?
Differentiate
y = ln(5x)
dy/dx = 1/x
Graph of sec x
Graph of cosec x
Graph of cot x
Domain and range of sec x
Domain: x ∈ R, x ≠ any odd multiple of 90
Range: between -1 and 1
Domain and range of cosec x
Domain: x ∈ R, x ≠ any multiple of 180
Range: between -1 and 1
Domain and range of cot x
Domain: x ∈ R, x ≠ any multiple of 180
Range: y ∈ R
Differentiate y = akx
dy/dx = akx k ln(a)
nth term of a geometric sequence
arn-1
Equation for length of a line
[ (x1 + x2)2 + (y1 + y2)2 ]1/2
Arc Length equation
arc length = 2πr × (θ/360)
if in radians then (θ/2π)
Note
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