Natural Domain

Presentation

•

Mathematics

•

10th Grade

•

Hard

Shayna Wright

Used 9+ times

FREE Resource

4 Slides • 5 Questions

Natural Domain

Domain restrictions occur when the function is undefined.

A fraction is undefined when the denominator is zero.

$f\left(x\right)=\frac{1}{x},\ x\ne0$
$f\left(x\right)=\frac{x-9}{\left(x-2\right)\left(x+3\right)},\ x\ne-3,\ 2$

Multiple Select

For what value(s) is the function undefined? Check ALL that apply

f\left(x\right)=\frac{3x-5}{x\left(2x-3\right)}

$x\ne0$

$x\ne\frac{3}{2}$

$x\ne\frac{5}{3}$

None: The Domain of this function is All Real Numbers

Multiple Select

For what value(s) is the function undefined?

f\left(x\right)=\frac{3x-5}{x^2-5x+6}

$x\ne3$

$x\ne2$

$x\ne6$

$x\ne-1$

A radical with an EVEN index must be positive or zero. It is undefined when the radicand is negative.

$f\left(x\right)=\sqrt{x}\ ,\ x\ge0$
$f\left(x\right)=3\sqrt{x-4}+5\ ,\ x\ge4$
However; $f\left(x\right)=\sqrt{x^2+3}$ has a domain of All Real Numbers because the radicand cannot be negative (no matter what we substitute for x.)

Multiple Choice

Determine the domain of the function.

f\left(x\right)=\sqrt{2x-3}

$x\ge\frac{3}{2}$

$x>\frac{3}{2}$

$x\ne\frac{3}{2}$

$x\le\frac{3}{2}$

Multiple Choice

What is the domain of the function?

f\left(x\right)=4\sqrt{-x+3}

$x\ge3$

$x>3$

$x\le3$

All Real Numbers

When a radical appears in the denominator of a fraction, we must consider both criteria. The radicand must be positive and CANNOT be zero.

$f\left(x\right)=\frac{1}{\sqrt{x}},\ x>0$ notice the $\ge$ is not just >
$f\left(x\right)=\frac{3x}{\sqrt{x-2}},\ x>2$

Multiple Choice

Determine the domain of the function.

f\left(x\right)=\frac{2x}{\sqrt{2x-8}}

$x>-4$

$x\ne4$

$x<4$

$x>4$

Natural Domain

Domain restrictions occur when the function is undefined.

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