Find DoMainof a Function

Perils of the Do Man: Rational Abe & Radical Surfer

Find Domain of Rational Function:

Rational AbeProblem: Abe’s Railroad

𝑓 (𝑥 )= 1

#Find Domain of Rational Function:

Rational AbeProblem: Abe’s Railroad

𝑓 (𝑥 )= 1

#Find Domain of Rational Function:

Rational AbeProblem: Abe’s Railroad

𝑓 (𝑥 )= 1

Problem: Denominator 0Abe Can’t Go Bottomless!

Solution: Build a Bridge

Solution: Build a Bridge

# #

Solution: Build a Bridge

Build a bridge ( , # ) ( # , )Restricted Value: # makes the denominator = 0

# #

Solution: Build a Bridge

Build a bridge ( , # ) ( # , )Restricted Value: # makes the denominator = 0

# #

Radical SurferProblem: Alligator on Beach

Find Domain of Radical Function:

𝑓 (𝑥 )=√

Radical SurferProblem: Alligator on Beach

Find Domain of Radical Function:

𝑓 (𝑥 )=√

Radical SurferProblem: Alligator on Beach

Find Domain of Radical Function:

𝑓 (𝑥 )=√

Radical SurferProblem: Alligator on Beach

Find Domain of Radical Function:

𝑓 (𝑥 )=√ Problem: Radicand > 0Square Roots of Negative Numbers is not real.

The Surfer Must be REAL!

Solution: Grab the Board & Hit the Wave

Solution: Grab the Board & Hit the Wave

#

Solution: Grab the Board & Hit the Wave

#The beach # is where the radicand = 0 [# , ) East Coast

Solution: Grab the Board & Hit the Wave

#The beach # is where the radicand = 0 [# , ) East Coast

OR When x starts out negative then: ( , # ] West Coast

8.2 Domain of FunctionIn most cases: Domain is All Real Numbers; (-∞,∞)

Two Exceptions: FRACTIONS OR SQUARE ROOTS?

A. Rational: Fractions → Denominator ≠ 0x ≠ # ; ( 3 ∞, #) U ( # ,∞) Build a Bridge

B. Radical: Square Roots → Radicand > 0 x > # ; [ # , ∞) or ( 3 ∞ , #]

(when x is negative)

Solve Inequalities:#1 Rule: Multiply or Divide by a negative. Then Flip the Inequality.