unit 6 test

Question 1

6.1 reminders (finding domain)

Answer 1

equal denominatior to 0 and factor

write out in set builder or interval notation

if statement is false when set to 0, it’s all real numbers

Question 2

6.1 reminders (setting to lowest terms)

Answer 2

fundamental property: a/b=ac/bc
ex: 15/20= 3x5/4x5 = 3/4

if there are opposites in a fraction, expression = -1 except for r-2/r+2

Question 3

6.1 reminders (multiplying and dividing expressions)

Answer 3

multiply:
-cross multiply and factor completely
-make sure to keep expressions separate for easier solving

divide:
-key, change,flip
-factor and separate expressions as much as possible
-all individual components are separate

Question 4

6.2 reminders (adding and subtracting expressions)

Answer 4

-expressions must have a LCD first
-factor completely
- write restrictions and lowest terms as
___;x=/___

Question 5

6.3 reminders (complex fractions)

Answer 5

-convert to regular division between fractions
-make sure to separate other parts of the expression with parentheses and apply usual rules

Question 6

6.4 (solving equations)

Answer 6

-make sure to find a LCD
-LCD won’t be needed for final answer
-factor completely (no crossing out)
-check over work
-if a numerator equals what could make the denominator = 0, erase the answer or declare it no solution

Question 7

6.5 (applications of rational expressions)

Answer 7

• to find a specific variable, isolate it to one side of the expression
  -when numerators are identical and equal to one another, they can be eliminated
  -make sure to multiply both sides by the LCD
  -distribute fully
  -keep digits and variables separate with a multiplication sign when multiplying

Question 8

6.5 (ratios)

Answer 8

-ratio symbol= division symbol
-let unknown variable equal x
-when creating proportions, keep all relevant elements on the same side
-if there’s an amount started, add that to unknown variable
ex. 8/156=x+3/200

Question 9

6.6 variations

Answer 9

formulas
-direct variation: y=kx
-inverse variation: y= k/x
-__+square variation: ___x^2
-joint variation: y= kxz

-K or constant goes after =
-when something is squared, must stay before reaching final solution
-find constant, then plug into the applied formula