Managerial Mathematics(QQM 1023)
Tutorial 2 – Introduction to Function

1. Which of the following equations define y as a function of x?

a) y = 3x + 1 b) y = 2x2 c) y = 5 d) y = 2x e) x = 3

f) y2 = x g) y = x3 h) y = [pic] i) y = x j) y = [pic]

2. Determine types of function for the following equations: a) f(x) = 2 b) g(x) = [pic] c) f(x) = 4 – x d) f(x) = 2x e) g(x) = x2 + 3x f) h(x) = 2x g) h(x) = ex h) g(x) = x2 i) h(x) = [pic]

j) h(x) = [pic]

3. Find the values for each function based on the inputs given:

a) f(x) = 3x – 5, f(-1) and f(0) b) g(x) = x2 – 3x, g(4) and g(-2) + g(0)

c) f(t) = [pic], f(2) and f(0) d) g(t) = 2t , g(3) and g(0) – g(1)

e) h(x) = [pic] , h(-1) and h(3) f) h(x) =[pic] , h(-3) and h(1) + h(0)

g) g(x) = [pic] , g(1) and g(-1) h) f(x) = [pic] , f(1) and f(9) – f(-1)

i) g(x) = [pic] , g(2) and g(0) + g(-2) j) f(x) = 5 , f(0) and f(-1) – f(5)

4. Find the domain of each function: a) f(x) = [pic] b) h(x) = [pic] c) g(x) = [pic] d) g(x) = [pic] e) h(x) = [pic] f) f(x) = [pic] g) f(x) =[pic] h) h(x) = [pic] i) f(t) = 4t2 – 5 j) f(x) = 4 k) g(x) = [pic] l) f(x) =[pic] m) f(x) = [pic] n) h(x) = [pic]

5. Based on the graphs, determine the domain and range of the given functions. a) y = x + 1 b) y = x2 c) y = [pic] d) y = x2 - 9

e) x + y = 1 f) y = 4 – x2 g) y = 2 h) f(x) = [pic]

6. If a RM 30,000 machine depreciates 2% from its original value each year, find a function f that expresses the machine’s value V after t years have elapsed.

Answer:

1 a) b) c) d) g) h) i) j)

2 a) constant b) rational c) linear d) linear e) quadratic f) exponential g) exponent h) quadratic i) compound j) linear

3 a) –8 and –5 b) 4 and 10 c) [pic] and 0 d) 8 and –1 e) 1 and 3 f) 2 and 9 g) 2 and 0 h) 9 and 10 i ) 4 and –4 j) 5 and 0

4 a) x ( R, x ( 0 b) x ( R, x ( [pic] c) x ( R d) x ( R, x ( 0, x ( 1 e) x ( R, x ( 3 f) x ( R, x ( -1, x ( -5 g) x ( R, x > 0 h) x ( R i) t ( R j) x ( R k) x ( R, x ( -8 l) 1 ( x ( 3 m) x ( R, x ( [pic] n) x ( R 5 a) D : x ( R , J : y ( R b) D : x ( R , J : y ( 0 c) D : x ( R, x ( 0 , J : y ( R, y ( 0 d) D : x ( R , J : y ( -9 e) D : x ( R , J : y ( R f) D : x ( R , J : y ( 4 g) D : x ( R , J : y = 2 h) D : x ( 0 , J : 0 ( y ( 2

6 [pic]

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