2-how-to-find-the-domain-of-any-function-mathbff

# Interactive video lesson plan for: ❤︎² How to Find the Domain of Any Function (mathbff)

#### Activity overview:

For Domain, you just need to watch out for Square Roots and/or Fractions!

1) a POLYNOMIAL (no square roots or fractions), i.e. f(x) = x^2 + 3x + 1, domain is "all real numbers."

2) a FRACTION (w/ no square root), i.e. f(x) = (2x+1)/(x^2+5x+6). Set bottom "not equal" to zero. Solve for x.

3) a SQUARE ROOT (w/ no fraction), i.e. f(x) = sqrt(x+1). Set part under root "greater than or equal to zero".

4) a FRACTION w/ A SQUARE ROOT ON BOTTOM, i.e. f(x) = (x^2+2x+3)/(sqrt(x+1)). Set part under root "greater than zero." Solve the inequality. NOTE THE DIFFERENCE: You must set it greater than zero, not "greater than OR EQUAL TO zero" because we can't have zero (or square root of zero) in the denominator.

5) a FRACTION w/ A SQUARE ROOT ON TOP, i.e. f(x) = (sqrt(x+1))/(x^2+4), i) Set the bottom "not equal to" zero & solve; ii) Set what's under the root "greater than or equal to zero" & solve; iii) Take intersection of your two solutions.

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