# How do you graph f(x)=sqrt(2x+3)?

Feb 17, 2017

See explanation

#### Explanation:

Build a table of values relating $y$ to $x$. You must take into account that what we really have is $y = \pm \sqrt{2 x + 3}$. Plot the points and draw the best line you can through those points.

Note that the x-intercept is where $y = 0 = \sqrt{2 x + 3}$

Also note that $\sqrt{0} = 0 \text{ "=>" } 2 x + 3 = 0$

$2 x = - 3$

${x}_{\text{intercept}} = - \frac{3}{2}$
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Lets suppose you do not have a calculator. Then you need to select values for $2 x + 3$ that are known squared values and adjust $x$ to give them.

This is the selection:
${\left(\pm 1\right)}^{2} = 1$
${\left(\pm 2\right)}^{2} = 4$
${\left(\pm 3\right)}^{2} = 9$
${\left(\pm 4\right)}^{2} = 16$
${\left(\pm 5\right)}^{2} = 25 \leftarrow$ stop at this one as they are getting a bit big

$\textcolor{b l u e}{\text{Set "2x+3=1" " =>" " 2x=-2" " =>" } x = - 1}$

$\text{ } \pm y = \pm 1 = \pm \sqrt{2 \left(- 1\right) + 3}$
" "color(brown)(=> (x,y) = (-1,+1)" " &" " (-1,-1))
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$\textcolor{b l u e}{\text{Set "2x+3=4" " =>" " 2x=+1" " =>" } x = + \frac{1}{2}}$

$\text{ } \pm y = \pm 2 = \pm \sqrt{2 \left(\frac{1}{2}\right) + 3}$
" "color(brown)(=> (x,y) = (1/2,+2)" " &" " (1/2,-2))

................................................................................................
color(blue)("Set "2x+3=9" " =>" " 2x=+6" " =>" "x=+6/2

$\text{ } \pm y = \pm 3 = \pm \sqrt{2 \left(\frac{6}{2}\right) + 3}$
" "color(brown)(=> (x,y) = (6/2,+3)" " &" " (6/2,-3))

................................................................................................
color(blue)("Set "2x+3=16" " =>" " 2x=+13" " =>" "x=+13/2

$\text{ } \pm y = \pm 4 = \pm \sqrt{2 \left(\frac{13}{2}\right) + 3}$
" "color(brown)(=> (x,y) = (13/2,+4)" " &" " (13/2,-4))

................................................................................................
color(blue)("Set "2x+3=25" " =>" " 2x=+22" " =>" "x=+22/2

$\text{ } \pm y = \pm 5 = \pm \sqrt{2 \left(\frac{22}{2}\right) + 3}$
" "color(brown)(=> (x,y) = (22/2,+5)" " &" " (22/2,-5))

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Your graph should look like this: