Hi everyone!!! Just like i promise, we meet again. For this time, i will continue with chapter 3. Basically this chapter is about the reciprocal of each function. We will learn the characteristics of each reciprocal. For this 3.1 sub-unit we will learn the reciprocal of linear.......Let's get started!
Before getting to know the reciprocal of linear lets identified a linear function first. A linear function is a function with a highest degree of one. Let me give you an example of an equation of a linear; f(x)=2x-3 or maybe more simple, f(x)=x. The graph is like this:
Sorry, i cannot find a graph with scale on it. But this is how f(x)=x graph's looks like. So the reciprocal of this f(x)=x is just f(x)=1/x. The numerators must be a constant but not necessarily one, any number can be and the denominator is the linear function. Lets take a look how a reciprocal of f(x)=x looks like;
Wow!! Graph with scale and more amazing drawn on a graph paper.....So, this is how a reciprocal of linear looks like. Okay now it is time to identify the characteristic of the graph.
- The restriction on the domain - the denominator cannot equal to zero, so x cannot equal to zero.
- The asymptotes - x=0 is the vertical asymptote, while y=0 is the horizontal asymptote.
- Domain and range - {x E R, x cannot equal to 0}, {y E R, y cannot equal to 0}
- The end behaviour -as x à 0 from the left, y à ∞, as x à 0 from the right, y à −∞, as x à∞ from the left, y à 0, as x à−∞ from the right, y à 0
- The intercept - reciprocal does not have intercept.
0=1/x
x=1/0
x=1/0 is undefined so there are no x-intercept.
y=1/0
y=1/0 is also undefined so there are no y-intercept as well.
- As the graph approaches the vertical asymptote the slope of the graph become steeper.
- As the graph approaches the horizontal aymptote the slope of the graph become less steeper.
- Increasing interval= the interval when x increased, y increased.
- Decreasing interval= the interval when x decrease, y decrease.
So that's all for this chapter. I already describe the characteristics of the reciprocal. Look forward to my next post, as i will continue with chapter 3.2!! Bye!!
