Graphing Functions

[FallonXay]

Hi,

I'm having a little trouble with these domain/ range questions. I assume you solve these through graphing the functions. But how are you meant to know what these graphs look like, specifically graphs with roots in them? For example, I'm struggling with graphing root (sinx) or root(1  - 2sinx) or (x-8)^(-1/3).

Thanks.

[Syndicate]

Hi,

I'm having a little trouble with these domain/ range questions. I assume you solve these through graphing the functions. But how are you meant to know what these graphs look like, specifically graphs with roots in them? For example, I'm struggling with graphing root (sinx) or root(1  - 2sinx) or (x-8)^(-1/3).

Thanks.

Late reply:

You can graph by calculating where the graph is approaching infinite (so like asymptotes and stuff).
\( \sqrt{sinx} \). Well from this function, you can already tell that sin(x) must be a positive number (otherwise you will not be able to graph this in a real plane).

1. Start with the axis intercepts.
- In this case: y-int = 0, and x-int = 0, pi, 2pi, 3pi etc...
Therefore, you graph goes from 0 to pi, then 2pi to 3pi. Since there is a square-root, the graph will be a bit more circular (so, the top bit will look like semi circles).

You can calculate the T.P. using the chain rule.

Similar case for \(\sqrt{1-2sinx} \)
y- int at (1,0), and x-int at -7pi/6, pi/6, 5pi/6, 13pi/6 etc...
Again there will be parts where the graph doesn't continue (like between pi/6 and 5pi/6 [not inclusive]).

As for \( (x-8)^{-\frac{1}{3}} \), you will have two asymptotes. One at x = 8, and the other at y = 0 (as the highest degree of the numerator is smaller than the highest degree of the denominator).

Calculate the y-int, and sketch the graph over an infinite interval (this function is a rectangular hyperbola because (x-8) has a negative odd exponent). 

I hope it make sense (I am a bit rusty on this  )