Differential Calculus - Functions and Their Graphs

Sabtu, 20 Juni 2020

Functions: f, g, y, u, v

Argument (independent variable): x

Real numbers: a, b, c, d

Natural number: n

Angle: α

Inverse function: f ^{– 1}

 

 

Functions and Their Graphs

 

• Even Function

   f (– x) = f (x) 

 

• Odd Function

   f (– x) = – f (x)

 

• Periodic Function

   f (x + nT) =  f (x)

 

• Inverse Function

   y = f (x) is any function, x = g (y) or y = f ^{– 1} (x) is its inverse function.

 

Figure

 

 

• Composite Function

   y = f (u), u = g (x), y = f (g (x)) is a composite function.

 

• Linear Function

   y = ax + b, x ∈ R, a = tan α is the slope of the line, b is the y-intercept.

 

Figure

 

• Quadratic Function

   y = x², x ∈ R.

 

Figure

 

• y = ax² + bx + c, x ∈ R

 

Figure

 

 

• Cubic Function

   y = x³, x ∈ R

 

Figure

 

• y = ax³ + bx² + cx + d, x ∈ R

 

Figure

 

• Power Function

   y = xⁿ , n ∈ N

 

 

Figure

 

 

Figure 

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Labels: Mathematician

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