# How do you graph y=4/3sqrt(x)?

Apr 28, 2017

Try different x values and plot accordingly

#### Explanation:

If you assign $x = 1$ you will get your function $y = \frac{4}{3}$

If you assign $x = 2$ you will get $y = 1.886$

If you assign $x = 3$ you will get $y = 2.309$

etc. On the negative side your function is not defined.

Now plot accordingly.

graph{(4/3)sqrtx [-3, 20, -2, 10]}

Apr 28, 2017

See explanation

#### Explanation:

Suppose the square root of $x$ is $a$. Then the value of a may be positive or negative.

Example

${\left(- 2\right)}^{2} = {\left(+ 2\right)}^{2} = 4$

So $\sqrt{4} = \pm 2$

Thus $y = \frac{3}{4} \sqrt{x} \text{ }$ is really $y = \pm \frac{3}{4} \sqrt{x}$

If you wish the numbers to remain in the real domain $\to \mathbb{R}$ then

$y = \pm \frac{3}{4} \sqrt{- x}$ is not permitted

That is: $x$ is a squared value but the squared value must not itself be negative.
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Consequently the graph is split into 2 parts

First part: $\text{ } y = + \frac{3}{4} \sqrt{x}$
Second part $y = - \frac{3}{4} \sqrt{x}$