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MATH1252 Homeowork 1

Due Tuesday 7/7

1. Give the domain of each following function

(a) f (x) = 2x + 3

(b) f (x) =

(c) f (x) =

4

x2 −4x−5

q

x2

9−x2

2. For each of the following, find f (x + h) and

f (x+h)−f (x)

h

(a) f (x) = −4×2 + 3x + 2

(b) f (x) =

1

x2

3. Classify the functions as even or odd

(a) f (x) = −4x

(b) f (x) = 5×2

(c) f (x) = x3 − x

4. Complete the square and determine the vertex

(a) y = x2 − 6x − 11

(b) y = 4×2 − 20x − 7

5. Maximizing Revenue:A charter flight charges a fare of $200 per person plus $4

per person for each unsold seat on the plane.The plane holds 100 passengers. Let x

represent the number of unsold seats.

(a) Find an expression for the total revenue received for the flight R(x)

(b) Graph the expression from part (a)

(c) Find the number of unsold seats that will produce the maximum revenue.

6. Sketch a graph of f (x) = (x + 1)3 − 2

7. Find horizontal and vertical asymptotes and any holes if there exist.

(a) y =

(b) y =

1

x−3

6−3x

4x+8

8. Solve equations

(a) (e3 )−2x−1 = ex+11

(b) 2x

2 −4x

1 x−4

= ( 16

)

(c) log(2x − 1) + log x = 1

9. Graph y = 2e−x − 3

10. Evaluate each logarithmic function without using a calculator

(a) log3 81

(b) ln e3

11. Prove loga xr = r loga x

12. Decrease in bacteria: When an antibiotic ins introduced into a culture of 50,000

bacteria, the number of bacteria decreases exponentially. After 9 hours, there are

only 20,000 bacteria.

(a) Write an exponential equation to express the growth function y in terms of time

t in hours.

(b) In how many hours will half the number of bacteria remain?

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math

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