Homework Problems (Ch 2&3) Module 1 – Week 1 Exercise 2.5: Function and exponents 1. Graph the functions a) y = 16 + 2x b) y = 8 – 2x c) y = 2x +12 (In each case, consider the domain as consisting of nonnegative real numbers only) 5. Condense the following expressions: b) x^a\times x^b\times x^c c){\ \ x}^3\times y^3\times z^3 6. Find: b) \left(x^{1/2}\times x^{1/3}\right)/x^{2/3} Exercise 3.2: Single Unknown 2. Let the demand and supply function be as follows: a) Q_d= 51 – 3P b) Q_d=30-2P Q_s=6P-10 Q_s=-6+5P Find P* and Q* by elimination of variables. (Use fractions rather than decimals) 4. If (b + d) =0 in the linear market model, can an equilibrium solution be found by using (3.4) and (3.5)? Why or why not? Exercise 3.3: Nonlinear equations 1. Find the zeros of the following functions graphically: b) g\left(x\right)=2x^2-4x-16 4 c) For the following function determine if x = 1 is a root: 5. Find the rational roots, if any, of the following: b) 8x^3+6x^2-3x-1=0 6. Find the equilibrium solution for each of the following models: a) Q_d=Q_s Q_d=3-P^2 Q_s=6P-4 Exercise 3.5: More than one unknown 2. Let the national-income model be: Y=C+I_0+G C=a+b\left(Y-T_0\right) \left(a>0,\ \ \ \ 0
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Homework Problems (Ch 2&3) Module 1 – Week 1 Exercise 2.5: Function and exponents 1. Graph...
Homework Problems (Ch 2&3) Module 1 – Week 1 Exercise 2.5: Function and exponents 1. Graph the functions a) y = 16 + 2x b) y = 8 – 2x c) y = 2x +12 (In each case, consider the domain as consisting of nonnegative real numbers only) 5. Condense the following expressions: b) x^a\times x^b\times x^c c){\ \ x}^3\times y^3\times z^3 6. Find: b) \left(x^{1/2}\times x^{1/3}\right)/x^{2/3} Exercise 3.2: Single Unknown 2. Let the demand and supply function be as...
Exercise 3.2: Single Unknown 2. Let the demand and supply function be as follows: a) Q_d= 51 – 3P b) Q_d=30-2P Q_s=6P-10 Q_s=-6+5P Find P* and Q* by elimination of variables. (Use fractions rather than decimals) 4. If (b + d) =0 in the linear market model, can an equilibrium solution be found by using (3.4) and (3.5)? Why or why not? 3.4 Answer: P*_1 = 3 6/17 P*_2 - 3 8/17 Q*_1 = 11 7/17 Q*_2 = 8 7/17...
Exercise 3.3: Nonlinear equations 1. Find the zeros of the following functions graphically: b) g\left(x\right)=2x^2-4x-16 4 c) For the following function determine if x = 1 is a root: 5. Find the rational roots, if any, of the following: b) 8x^3+6x^2-3x-1=0 6. Find the equilibrium solution for each of the following models: a) Q_d=Q_s Q_d=3-P^2 Q_s=6P-4
Exercise 3.2: Single Unknown 2. Let the demand and supply function be as follows: a) Q_d= 51 – 3P b) Q_d=30-2P Q_s=6P-10 Q_s=-6+5P Find P* and Q* by elimination of variables. (Use fractions rather than decimals) 4. If (b + d) =0 in the linear market model, can an equilibrium solution be found by using (3.4) and (3.5)? Why or why not?
Exercise 2.5: Function and exponents 1. Graph the functions a) y = 16 + 2x b) y = 8 – 2x c) y = 2x +12 (In each case, consider the domain as consisting of nonnegative real numbers only) 5. Condense the following expressions: b) x^a\times x^b\times x^c c){\ \ x}^3\times y^3\times z^3 6. Find: b) \left(x^{1/2}\times x^{1/3}\right)/x^{2/3}
EXERCISE 2.4 1. Given $1 = {3,6,9, 52 = (a, b), and S3 = {m, n}, find the Cartesian products: (0) Sy x 52 (b) $2 x S3 (C) 53 x 51 5. If the domain of the function y=5+ 3x is the set (* 1<x< 9), find the range of the function and express it as a set. EXERCISE 2.3 3. Referring to the four sets given in Prob. 2, find: (a) S, US (c) S2 S3 () 54...
9. Graph the function defined by f(x) = 2 x +1 -3. Parent function: f(x) = x 1. f(x) = 2x +1 -3 Shift the graph to the left 1 unit 2. f(x) = 2 x +1 -3 Apply a vertical stretch multiply the y-values by 2) 3. f(x) = 2x+1-3 Shift the graph downward 3 units. 10. Graph the function defined by = (x) = -V3- x. Parent function y = x
2.9.19 If a function f has an inverse and f(-3) = 2, then what is f-1(2)? 7+(2)=0 2.9.33 2x+8 3x - 8 Consider the functions f(x) = 7and g(x)=3-. (a) Find f(g(x)). (b) Find g(f(x)) (c) Determine whether the functions f and g are inverses of each other (a) What is f(g(x))? f(g(x)) = (Simplify your answer.) % 2.9.27 For F(x)=x2-5, find each of the following a. f(0) b.-1(-5) c. (fof-1/(507) a. f(0) = -5 b.t-1(-5)=0
2. Sketch the graph of the following functions and find the values of x for which lim f(x) does not exist. b)/(x) = 1, x = 0 f(x)- 5, x=3 c) x2 x>1 2x, x> 3 d) f(x)-v e) (x)- [2x 1- sin x Discuss the continuity of the functions given in problem #2 above. Also, determine (using the limit concept) if the discontinuities of these functions are removable or nonremovable 3. Find the value of the constant k (using...
Use the graph of the function to find the indicated values. This figure has a wavy curved line graphed on the x y-coordinate plane. The x-axis runs from negative 2 times pi to 2 times pi. The y-axis runs from negative 6 to 6. The curved line segment goes through the points (negative 2 times pi, 0), (negative 3 divided by 2 times pi, 2), (negative pi, 0), (negative 1 divided by 2 times pi, negative 2), (0, 0), (1...