Family of curves

A Family of curves is a set of functions that depends not only on the variable $x$ but also on another parameter.

Example

A function equation $y=f(x)$ depends on a parameter that can be used with the function in different ways, e.g. can be added or multiplied:

• $f_a(x)=f(x)+a$
• $f_b(x)=f(x+b)$
• $f_c(x)=c\cdot f(x)$
• $f_d(x)=f(d\cdot x)$

Example

$f_a(x)=x^2+a$ (mit $a\in\mathbb{R}$)

• $\color{red}{f_3(x)=x^2+3}$
• $\color{green}{f_1(x)=x^2+1}$
• $\color{blue}{f_{-1}(x)=x^2-1}$
• $\color{black}{f_{-1.5}(x)=x^2-1.5}$