Graph and domain of $\frac{2}{7+\sqrt{x}}$

Question

How to sketch the graph of $\frac{2}{7+\sqrt{x}}$? Can anyone give me some hints ?

Answer 1

The domain is apparently the interval $[0, +\infty)$.

To sketch the graph take these values for $x$: $a, a+k, a+2k, a+3k, ...$ and calculate the respective values of the function: $f(a+ik)$, for $i=0,1,2,3,...$. Use $a=0$, while $k$ you can choose yourself e.g. you may take $k=0.1$ or $k=1$. Here $a$ is the initial value, $k$ is the step/increment. Finally connect the dots representing $f(a+ik)$. The smaller $k$ you pick, the more dots you'll get and the more precise your graph will be.

Answer 2

An R script to plot

f <- function(x){
return (2 / (7+sqrt(x)))
}
x <- seq(from = 0, to = 100,by = 0.1)
plot(x, f(x), type = "l")

Answer 3

You might like to look at the book by Gelfand, Glagoleva, and Shnol, 'Functions and Graphs' (pdf: http://www.cimat.mx/~gil/docencia/2012/calculo/functions_and_graphs_gelfand.pdf ) for more general strategies in graph sketching. The questions to ask are things like: What does the graph do as x goes to +/- infinity? Are there any undefined points? If there is a denominator, does it go to zero, meaning the graph 'blows up'? When is the graph increasing or decreasing? So where are the turning point? And so on...