graphing sqrt function

[Frankie Bailey]

Given the graph of the basic sqrt function: y=sqrt(x), one can graph the function:y=a(sqrt(x+b)) +c by observing the constants and perforforming shifts etc... on the base function.

If the function contains something like sqrt(4x-8), then one can factor to obtain 4(x-2), remove the sqrt 4 and graph the function, as usual.

Now, here is the question, how does one do this with a function that contains something like sqrt(2x-3) where a perfect square cannot conveniently be factored out?

y=sqrt(3x-5) +6 is an exercise in the textbook but no examples of this is given. It is listed as a "challenge."

 

[pappus]

Given the graph of the basic sqrt function: y=sqrt(x), one can graph the function:y=a(sqrt(x+b)) +c by observing the constants and perforforming shifts etc... on the base function.

If the function contains something like sqrt(4x-8), then one can factor to obtain 4(x-2), remove the sqrt 4 and graph the function, as usual.

Now, here is the question, how does one do this with a function that contains something like sqrt(2x-3) where a perfect square cannot conveniently be factored out?

y=sqrt(3x-5) +6 is an exercise in the textbook but no examples of this is given. It is listed as a "challenge."

1. This example asks you to re-write

\(\displaystyle y=\sqrt{3x-5} +6\)

into this form:

\(\displaystyle y=a \cdot \sqrt{x+b} +c\)

2. Compare:

\(\displaystyle \left|\begin{array}{rcl}y&=&\sqrt{3x-5} +6 \\ y&=&a \cdot \sqrt{x+b} +c\end{array}\right.\) ..... \(\displaystyle \implies\) ......\(\displaystyle \left|\begin{array}{rcl}y&=&\sqrt{3} \cdot \sqrt{x-\frac53} +6 \\ y&=&a \cdot \sqrt{x+b} +c\end{array}\right.\)

 

[Frankie Bailey]

Thank you. I did think of this but was not certain that "a" could be irrational.