Solving Literal Equations

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 $(0,\ 2)$ .

Solving Literal Equations: Polynomials

Simply put, you just need to treat all pronumerals as numbers. Then, use your knowledge with polynomials to solve them.

Example

Solve the following:

a) $x^{2}+k x+k=0$ ;

Using our knowledge of solution for quadratic functions, we know that

Linear Literal Equation Systems

In previous years, you are already equipped with the skills to solve simple linear equations like $4 y-\frac{(3 y+4)}{2}+\frac{1}{3}=\frac{5(4-y)}{3}$ , including their corresponding worded problems. The skills learnt are crucial and will be applied in the topics explored in this course.

A literal equation in $x$ is an equation whose solution will be expressed in terms of pronumerals rather than numbers.

In simpler terms, instead of solving

$2x+5=7$

instead you will be dealing with

$ax+b=c$

Solving Literal Equations

6.3 Families of Functions and Solving Literal Equations

Families of Functions and Solving Literal Equations

6.2 Literal Equation Systems: Polynomials

Solving Literal Equations: Polynomials

6.1 Revision for Linear Systems

Linear Literal Equation Systems