Applied Algebra Final Review: Equations, Inequalities, Functions, and Domain-Ranges Questions with Correct Answers

Applied Algebra Final Review: Equations, Inequalities, Functions, and
Domain-Ranges Questions with Correct Answers


Question 1:
Solve the equation 2 + 5(4v - 1) = -123
Answer:
To solve for v, first simplify: 2 + 20v - 5 = -123. Then, combine like terms: 20v - 3 = -123. Add 3
to both sides: 20v = -120. Finally, divide by 20: v = -6.


Question 2:
Solve the inequality -5(4 + 2x) ≤ -100
Answer:
Distribute -5: -20 - 10x ≤ -100. Add 20 to both sides:
-10x ≤ -80. Divide by -10 (remember to flip the inequality): x ≥ 8.


Question 3:
Determine the domain of the relation (-2, 1), (5, 8), (4, 3), (-2, 10)
Answer:
The domain is the set of all first elements in the ordered pairs: {-2, 5, 4}.


Question 4:
Determine the range of the relation (-2, 1), (5, 8), (4, 3), (-2, 10)
Answer:
The range is the set of all second elements in the ordered pairs: {1, 8, 3, 10}.


Question 5:
Is the relation (-2, 1), (5, 8), (4, 3), (-2,
10) a function?
Answer:
No, it is not a function because the input -2 corresponds to two different outputs (1 and 10).


Question 6:
Find f(2) for f(x) = 5(x - 7) - 1
Answer:
Substitute 2 into the function: f(2) = 5(2 - 7) - 1 =
5(-5) - 1 = -25 - 1 = -26.