SKETCH THE GRAPH OF F PLUS G FROM THE GRAPH

Problem 1 :

a) Sketch the graph of f + g. (Hint: For any x value, add the y values of f and g.)

b) What is the domain of f + g? Explain how you obtained your answer.

Solution:

a)

b)

Solution:

The domain of (f + g) is (-3, 6).

Problem 2 :

a) Sketch the graph of f - g. (Hint: For any x value, subtract the y values of f and g.)

b) What is the domain of f - g? Explain how you obtained your answer.

Solution:

a)

b) 

Solution:

The domain of (f - g) is (-3, 6).

Problem 3 :

Use the graphs below to compute the following values.

a) (f + g) (1)

b) (f - g) (2)

c) (g - f) (3)

d)  (f g) (4)

e)  (f / g) (1)

f) (g / f) (4)

Solution :

a) (f + g) (1)

(f + g) (1) = f(1) + g(1)

= 4 + 3

(f + g) (1) = 7

b) (f - g) (2)

(f - g) (2) = f(2) - g(2)

= 3 - 3

(f - g) (2) = 0

c) (g - f) (3)

(g - f) (3) = g(3) - f(3)

= 0 - 3

(g - f) (3) = -3

d)  (f g) (4)

(f g) (4) = f(4) g (4)

= 0 (4)

(f g) (4) = 0

e)  (f / g) (1)

(f / g) (1) = f(1) / g(1)

= 4/3

(f / g) (1) = 4/3

f) (g / f) (4)

(g / f) (4) = g(4) / f(4)

 = 4/0

(g / f) (4) = undefined

Problem 4 :

Use the graphs of the function f and g

a) Sketch the graph of (f + g)(x)

b) Sketch the graph of (f - g)(x)

Solution :

Ordered pairs for (f + g)(x) :

(-3, 3) (-2, 3) (-1, 1) (0, -1) (1, -3) (2, -3) (3, -3)

Ordered pairs for (f - g)(x) :

(-3, -1) (-2, -3) (-1, -3) (0, -3) (1, -3) (2, -1) (3, 1)

Problem 5 :

Betty is in the market for a new flat screen TV. She has two coupons that she can use to purchase the television. One coupon for 20% off the original price and the other coupon is for $100 off the original price.

a) Write the function p(x) to represent the discounted price of the television after the 20% off coupon is applied.

b)  Write the function d(x) to represent the discounted price of television after the $100 off coupon is applied.

c) Which coupon should Betty use ?

Solution :

Let x be the original price.

P(x) = (100 - 20)% of x

= 80% of x

= 0.80x

b)  d(x) = x - 100

c)  0.80x = x - 100

0.80x - x = - 100

-0.20 x = -100

x = 100/0.20

x = 500

If the price of TV is greater than 500, then 20% offer is the better deal.