Find the Domain and Range f(x)=x^3(x-2)^2(x+4)

$f (x) = x^{3} {(x - 2)}^{2} (x + 4)$

Step 1

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 2

The range is the set of all valid $y$ values. Use the graph to find the range.

Interval Notation:

$[- 352 - 160 \sqrt{5}, \infty)$

Set-Builder Notation:

${y | y \geq - 352 - 160 \sqrt{5}}$

Step 3

Determine the domain and range.

Domain: $(- \infty, \infty), {x | x \in ℝ}$

Range: $[- 352 - 160 \sqrt{5}, \infty), {y | y \geq - 352 - 160 \sqrt{5}}$

Step 4

Find the Domain and Range f(x)=x^3(x-2)^2(x+4)

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