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# 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).

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