Grade: 9 Subject: Math (Algebra I) Unit: Functions & Modeling Lesson: 6 of 6 SAT: AdvancedMath ACT: Math

Unit Quiz

Instructions

This quiz covers all concepts from the Functions & Modeling unit:

Complete all 10 questions. Click each to check your answer.

Question 1: If f(x) = 4x - 9, find f(-2).

Answer: f(-2) = -17

Solution: f(-2) = 4(-2) - 9 = -8 - 9 = -17.

Question 2: If g(x) = x² - 3x + 2, find g(4).

Answer: g(4) = 6

Solution: g(4) = (4)² - 3(4) + 2 = 16 - 12 + 2 = 6.

Question 3: A parking garage charges $5 plus $2 per hour. Write P(h) and find the cost for 4 hours.

Answer: P(h) = 2h + 5; P(4) = $13

Solution: P(h) = 2h + 5. P(4) = 2(4) + 5 = 8 + 5 = 13 dollars.

Question 4: If f(x) = 3x + 2 and g(x) = x - 4, find f(g(5)).

Answer: f(g(5)) = 5

Solution: First, g(5) = 5 - 4 = 1. Then f(1) = 3(1) + 2 = 5.

Question 5: For h(x) = 2x + b, if h(3) = 11, find b.

Answer: b = 5

Solution: 2(3) + b = 11. 6 + b = 11. b = 5.

Question 6: A tank has 500 gallons and loses 20 gallons per day. Write W(d) and find when it's empty.

Answer: W(d) = 500 - 20d; empty at d = 25 days

Solution: Set 500 - 20d = 0. 500 = 20d. d = 25 days.

Question 7: If f(x) = |2x - 6|, find f(1) + f(5).

Answer: f(1) + f(5) = 8

Solution: f(1) = |2(1) - 6| = |-4| = 4. f(5) = |2(5) - 6| = |4| = 4. Sum = 8.

Question 8: If f(x) = x² - 1, find f(2a).

Answer: f(2a) = 4a² - 1

Solution: f(2a) = (2a)² - 1 = 4a² - 1.

Question 9: A company's profit is P(x) = 15x - 200 where x is units sold. How many units to break even?

Answer: 14 units (rounding up from 13.33)

Solution: Set P(x) = 0: 15x - 200 = 0. 15x = 200. x = 200/15 = 13.33. Need 14 units to profit.

Question 10: Given the table: x = {0, 1, 2, 3}, f(x) = {-1, 2, 5, 8}. What is the rule for f(x)?

Answer: f(x) = 3x - 1

Solution: The pattern increases by 3 each time. Testing: f(0) = 3(0) - 1 = -1. f(1) = 3(1) - 1 = 2. Confirmed.