University:
College Entrance Preparation
Course:
ACT Preparation (Mathematics)
Academic year:

2024
Views:

136

Pages:

4
Author:

FrextWhestembki

**Lesson 4.2 • Function Notation** **Name:** **Period:** **Date:** **Key** 1. Determine whether or not each graph represents a function. Explain how you know. a. Yes b. No c. No 2. Find each of the indicated function values. a. If f(x) = √(4x + 1), find f(0), f(2), f(5), and f(-7). b. If f(x) = -x² + 3x + 5, find f(-3), f(0), f(2), f(7/5), and f(8). c. If f(x) = 2 / (x - 4)², find f(-4), f(0), f(5), f(8), and f(24). [Image of a graph] d. x when f(x) = 7 e. x when f(x) = -19 f. f(x + 2) = -5 g. f(2x) = 35 h. f(x - 3) = 5 i. x when f(x) = 15 j. x when f(x) = -21 3. Define variables and write a function that describes each situation. a. You drive on an interstate highway with your cruise control set at 65 miles per hour and do not need to stop or alter your speed. f(h) = 65h b. You rent a small moving van to move your belongings to your new apartment. The rental company charges $45 a day plus $0.22 a mile to rent the van. f(m) = 45 + 0.22m 4.2. Exercise 4 a. f(12) = 18 (R) b. f(25) + f(26) = 2 + 3 = 5 (E) c. 2f(22) = 2(11) = 22 (N) d. (f(3) + 11) / √f(3+1) = (9 + 11) / √(16) = 20 / 4 = 5 (E) e. f(1+4) / (f(1) + 4) = (5) / (1 + 4) = 5 / 5 = 1 (D) f. x when f(x+1) = 26 x + 1 = 6 x = 5 (E) g. √f(21) + f(x+3) = 52 √7 + f(x+3) = 52 f(x+3) = 52 - √7 f(6) = 52 - √7 x + 3 = 6 x = 3 (C) h. x when 2/f(x+3) = 2 2 / f(x+3) = 2 f(x+3) = 1 f(6) = 1 x + 3 = 6 x = 3 (C) i. x when f(2x) = 4 f(2) = 4 2x = 2 x = 1 (A) j. f(f(2) + f(3)) f(4 + 9) = f(13) = 18 (R) k. f(4) - f(25) = 22 - 2 = 20 (T) l. f(f(5) - f(1)) f(24 - 1) = f(23) = 5 (E) m. f(4.6) + f(4.4) f(5) + f(4) = 2 + 16 = 18 (S) **Function Practice** For a-f, tell if it's a function. If it is, find the y-value when x = 2 and find the x-value when y = 3. Use function notation. a. [Image of a parabola] Function. a(2) = 2 a(1) = 3 b. [Image of a circle] Nope! c. [Image of a set of points] Function. c(2) = Undefined c(1) = 3 c(3) = 3 d. [Image of a relation] Function d(2) = 3 d(2) = 3 e. [Image of a relation] Function e(2) = 2 e(_)=3 is undefined f. [Image of a relation] Nope! Tell if each relation below is a function. If it's not, tell why not. g. Independent variable: the age of each student in the class. Dependent variable: the height of each student. No, b/c 2 people of same age could be different heights. h. Independent variable: an automobile in the state of Kentucky Dependent variable: that automobile's license plate number.