Math Family of curves Family of curves

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.


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:

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


For each value of the additional parameter you get your own function graph.


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

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