## 6.3 Families of Functions and Solving Literal Equations

#### Families of Functions and Solving Literal Equations

- For instance, y=2 x^{3},\ y=-\frac{1}{4} x^{3} can all belong to a family function f(x)=k x^{3},\ k \neq 0.

- Functions from the same family would exhibit some similarities. Apart from the general shape of its graph, they might share some other things, such as a same intercept, a same asymptote, and so on.

- Literal equations can also be applied on the 3 types of functions we learnt for various things; it is simply a combination of all the knowledges you have learnt.

Example

**Let f: R \rightarrow R, and f(x)=m x+2 where m \in R^{+}. Find: **

**a) Its x-intercept; **

**b) The values of m where its x-intercept is lesser than 2; **

**c) Its inverse function; **

**d) The equation of the line perpendicular to f(x) at (0,\ 2).**