Deck 3: Functions and Graphs

Question 1

If f(x)=
- 2x + 3,find:
(a)the domain
(b)f(2)
(c)f(-2)
(d)f
(e)f(
)
(f)f(s + 1)
(g)f(x + h)

Answer 1

(a)all real numbers
(b)3
(c)11
(d) (e) - + 3
(f) + 2
(g) + 2hx + - 2x - 2h + 3

Question 2

The domain of f(t)= is

A) all real numbers
B) all real numbers except 0
C) all real numbers except 2
D) all real numbers except 4
E) all real numbers except 2 and 4

Answer 2

all real numbers except 4

Question 3

If f(x)= 5 - 8x,find:
(a)the domain
(b)f(1)
(c)f(-2)
(d)f
(e)f(t)
(f)f(x + 2)

Answer 3

(a)all real numbers
(b)-3
(c)21
(d)0
(e)5 - 8t
(f)-11 - 8x

Question 4

If g(x)=
,find g(x - 1)

Question 5

Given the function f(x)=
+ 4x + 2,find:
(a)the domain
(b)f(0)
(c)f(3)
(d)f(-2)
(e)f(-
)

Question 6

If f(x)= 4 -
,find

Question 7

Given the function F(t)=
,find:
(a)the domain
(b)F(-3)
(c)F(13)
(d)f(
+ 1)

Question 8

Find the domain of the function: f(q)=

Question 9

If f(x)= 4
+ 6x,find f(3s).

Question 10

Find the domain of the function: f(x)=

Question 11

Find the domain of the function: f(x)=

Question 12

If f(x)= 3x - 1,find

Question 13

If g(x)=
,find:
(a)the domain
(b)g(0)
(c)g(-4)
(d)g
(e)g(
)

Question 14

If f(x)=
+ 2x - 6,find

Question 15

The domain of f(x)= is

A) all real numbers
B) all real numbers except 6
C) all real numbers except 0
D) all real numbers except 0 and 3
E) all real numbers except 0, 3, and 6

Question 16

If g(s)=
- s,find:
(a)the domain
(b)g(0)
(c)g(3)
(d)g(-4)
(e)g

Question 17

For the equation 4y =
,(a)is y a function of x? (b)Is x a function of y?

Question 18

If x +
- 5 = 0,then x is a function of y.

Question 19

Find the domain of the function: f(t)=

Question 20

Find the domain of the function: f(t)=

Question 21

Find the domain:

Question 22

Let g(x)=
,find

Question 23

If f(x)= - - 2x - 6,then f(2)- f(t)=

A) + 2t - 8.
B) - - 2t + 4.
C) - 2t + 4.
D) - + 6t - 2.
E) -4 - 4t + 6.

Question 24

The domain of f(s)= is all real numbers s such that

A) s ≥
B) s ≤
C) s ≥
D) s ≤
E) s ≥ -

Question 25

The domain of f(q)= is

A) all real numbers
B) all real numbers except 1 and -1
C) all real numbers except -4
D) all real numbers except -2 and 2
E) all real numbers except -1, 1, and -2

Question 26

If f(x)= + 3x - 8,then
=

A) 0.
B) 1.
C) 2x + h + 3.
D) 4x + 3h - 2.
E)

Question 27

Exactly how many of the following equations define y as a function of x?
(a)y = 7 - x
(b)
= 4x
(c)y =
(d)
= y + 4

A) none
B) one
C) two
D) three
E) all

Question 28

If f(x)= + x,then f(-2)=

A) 0.
B) -2.
C) 3.
D) -7.
E) 7.

Question 29

If F(t)= ( +
,then F(
+ 1)=

A) ( +
B) ( + + 4.
C) ( +
D) ( + + 1.
E) ( + +

Question 30

If f(t)= (t + ,then f(t - 3)=

A) + 8t + 19
B) + 8t + 13.
C) + 4t + 13.
D) + 2t + 1.
E) + 1 + 1.

Question 31

If g(x)= 2 - 3x + 4,then g(0)- g(2)=

A) 2.
B) -2.
C) 0.
D) -14.
E) 14.

Question 32

Which equation below defines y as a function of x?

A) = y
B) + = 9
C) y = ±
D) 3x - = 0
E) 3y - = 0

Question 33

Find the domain of the function: F(x)=

Question 34

Find the domain of the function: f(x)=

Question 35

The domain of f(x)= consists of all real numbers x such that

A) x ≥
B) x ≥
C) x >
D) x ≥ -
E) x > -

Question 36

If f(x)= 2 - 3x + 4,then f(x + 1)=

A) 2 - 3x.
B) 2 - 3x + 5.
C) 2 + x + 6.
D) 2 + x + 3.
E) 2 + 4x + 7.

Question 37

If f(x)= ( +
,then f
=

A) -1.
B) 0.
C) 2.
D) 3.
E) 4.

Question 38

If f(x)= - 3x + 4,then f (2 + h)- f(2)=

A) + h.
B) + h - 4.
C) h.
D) - 3h - 4.
E) - 3h + 4.

Question 39

The domain of the function f(x)= is

A) all real numbers ≥ 2
B) all real numbers ≥ -2
C) all real numbers ≥ -2 except 4
D) all real numbers ≥ 2 except 4
E) all real numbers except 4 and -4

Question 40

If f(x)= 4x + 5,then =

A)
B) 0.
C) 1.
D) 4.
E) 4h.

Question 41

The height of an object thrown in the air depends on the time since it's been thrown.For a particular situation the height in meters of an object after t seconds can be represented by h(t)= 20t - 4.9
.
(a)What is the domain of this function out of context?
(b)What is the domain of this function in the given context?
(c)Find h(s),h(s + 2),and h(s + 6).
(d)Use an equation to describe what happens to the height if the time increases by a constant d.

Question 42

Suppose the weekly supply function for a large pizza at a local pizza parlor is p =
.
(a)How many large pizzas will be supplied if the price is $12.50 per pizza?
(b)How many large pizzas will be supplied if the price is $18.75 per pizza?
(c)How does the amount supplied change as the price increases?

Question 43

If f(t)= 1.9
- 3.1x + 2.01,then find f(x + 1.1).

Question 44

The speed you must travel for a given amount of time depends on the distance you must cover.
(a)Write a function r(d)for the speed if the time is 5 hours and the distance covered is d.
(b)What is the domain of this function out of context?
(c)What is the domain of this function in the given context?
(d)Find r(x),r
and r
,.
(e)What happens to the speed if the distance is reduced (divided)by a constant c? Describe using an equation.

Question 45

If f(x)=
,then find
and simplify.

Question 46

The perimeter of a square depends on the length of its side.
(a)Write a function p(l)for the perimeter of a square when the length of its side is l.
(b)What is the domain of this function out of context?
(c)What is the domain of this function in the given context?
(d)Find p(x),p(2x)and p(3x).
(e)What happens to the perimeter of a square when the side is scaled by a factor s? Describe using an equation.

Question 47

The elapsed time in seconds since January 1,2000 at 12:00 a.m.depends on the elapsed hours since January 1,2000 at 12:00 a.m.
(a)Write a function e(h)for the elapsed seconds since January 1,2000 at 12:00 a.m.when the elapsed hours are h.
(b)What is the domain of the function out of context?
(c)What is the domain of this function in the given context?
(d)Find e(t),e(-t),e(100t),and e(-100t).
(e)What does multiplying the elapsed hour by -1 mean?

Question 48

If f(x)= 1.05
+ 7.5
- 1.9,then find f(-0.5)

Question 49

The height of an object thrown in the air depends on the time since it has been thrown.For a particular situation the height in meters of an object after t seconds can be represented by h(t)= 20t - 4.9
.
(a)What is the height of the object if the time is x seconds?
(b)If the time is increased by 2 seconds,how much higher is the object?
(c)How much higher is the object per second increase?
(d)If the time is increased by h,how much higher is the object?
(e)How much higher is the object per unit increase?

Question 50

Suppose the yearly demand function for an artist's paintings is p =
.
(a)If the current prices is $200.00 per painting,how many paintings are sold each year?
(b)If the artist wants to sell 4 paintings per year,what should the price be?

Question 51

Suppose the weekly demand function for a pound of the house blend coffee at a local coffee shop is p = 15 -
.
(a)If the current price is $11.25 per pound,how much coffee is sold each week?
(b)If they are selling 180 pounds of coffee each week,what is the current price?
(c)If the owner wants to sell 300 pounds of coffee each week,what should the price be?

Question 52

The area of a circle depends on the length of its radius.
(a)Write a function a(r)for the area of a circle.
(b)How many square units of sod are needed to cover a circular grass area of radius x?
(c)If the radius of the circular grass area is increased by 2 feet,how much more sod is needed?
(d)How much more sod is needed per foot increase?
(e)If the radius of a circular grass area is increased by h,how much more sod is needed?
(f)How much more sod is needed per unit increase?

Question 53

The time it takes to go a given distance depends on the rate.
(a)Write a function t(r)for the time it takes if the distance is 400 miles and the rate is r miles per hour.
(b)How much time is needed when the rate is x?
(c)If the speed is increased by 10 miles per hour,how much less time is needed?
(d)How much less time is needed per mile per hour increase?
(e)If the speed is increased by h,how much less time is needed?
(f)How much less time is needed per unit increase?

Question 54

The proceeds from an event depend on the number of people who attend.
(a)Write a function p(n)for the proceeds if each ticket costs $8.00 and the number of tickets sold is n.
(b)What is the domain of this function out of context?
(c)What is the domain of this function in the given context?
(d)Find p(c),p(c + 5),and p(c + 25).
(e)What happens to the proceeds when the number who attend increases by a constant m? Describe using an equation.

Question 55

The perimeter of a square depends on the length of its side.
(a)Write a function p(l)for the perimeter of a square.
(b)How much linear fencing material is needed to fence a square garden of length x?
(c)If the sides of the square garden are increased by 3 feet,how much more linear fencing material is needed?
(d)How much more linear fencing material is needed per foot increase?
(e)If the sides of the square garden is increased by h,how much more linear fencing material is needed?
(f)How much more linear fencing material is needed per unit increase?

Question 56

In the equation
+
= 17; (a)Is x a function of y? (b)Is y a function of x?

Question 57

In the equation
+ 2x + 3xy +
= 11,is x a function of y?

Question 58

The weekly salary of an hourly employee depends on the number of hours worked.Employers are required to pay time and a half if an employee works over 40 hours per week.Suppose an employer refuses to pay time and a half and time cards are recorded in half-hour increments.
(a)Write a function s(h)for the weekly salary if a person's hourly pay is $12.25 and the number of hours worked is h.
(b)What is the domain of this function out of context?
(c)What is the domain of this function in the given context?
(d)Find s(t),s(t - 5),and s(t - 7).
(e)What happens to the salary if the work time decreases by a constant m? Describe using an equation.

Question 59

Let f(t)=
- 1,find (a)f(3t); (b)3 × f(t)

Question 60

Suppose f(x)=
+ 3xy -
.Find f(y).

Question 61

Under certain conditions,if two brown-eyed parents have exactly four children,the probability P that exactly r of them are blue-eyed is a function of r and is given by P(r)=
.
Find the probability that exactly one child will be blue-eyed.

Question 62

Given the function F(x)=
find:
(a)the domain
(b)F(2)
(c)F(-2)
(d)F(5)

Question 63

Suppose the yearly supply function for a particular actor to star in a film is p = 150,000x.
(a)How many films per year is the actor willing to produce if he earns $300,000 per film?
(b)How many films per year is the actor willing to produce if he earns $900,000 per film?
(c)How does the amount supplied change as the price increases?

Question 64

Find the domain of the function f(x)= 6.

Question 65

For the polynomial function f(x)=
+
,
Find: (a)the degree,and (b)the leading coefficient

Question 66

If g(x)=
,find g(-5).

Question 67

Given the function G(x)=
find:
(a)the domain
(b)G(0)
(c)G(6)
(d)G(-4)
(e)G(-10)

Question 68

The response R to a shock of intensity I is a number estimated by R = f(I)=
.
(a)Express f(2
)in terms of f(
).
(b)What effect does the doubling of intensity have on response?

Question 69

Given the function f(x)=
find:
(a)the domain
(b)f(1)
(c)f(2)
(d)f(3)
(e)f(0.1)

Question 70

Find: (a)the degree and (b)the leading coefficient of the polynomial function
P(x)= -
+ 6
- 9
+ 7x + 3

Question 71

Find: (a)the degree and (b)the leading coefficient of the polynomial function f(x)= 5x + 7.

Question 72

Under certain conditions,if two brown-eyed parents have exactly four children,the probability P that exactly r of them are blue-eyed is a function of r and is given by P(r)=
.
Find the probability that exactly thee children will be blue-eyed.

Question 73

Given the function f(x)=
find:
(a)the domain
(b)f(0)
(c)f(1)
(d)f
(e)f
(f)f

Question 74

If f(x)= 7,find f(14).

Question 75

If f(x)=
+ 2x,find: (a)f(1)and (b)f(-1).

Question 76

If f(x)=
,find
(a)f(-2)
(b)f(0)
(c)f
(d)f(1)
(e)f(5)

Question 77

Find: (a)the degree and (b)the leading coefficient of the polynomial function f(x)= 7 +
-
.

Question 78

For the polynomial function f(x)= 4 - 6x -
,
Find: (a)the degree,and (b)the leading coefficient

Question 79

Suppose the yearly supply function for paintings from an artist is p = 3000x.
(a)How many paintings per year will be supplied if the price is $21,000 per painting?
(b)How many paintings per year will be supplied if the price is $51,000 per painting?
(c)How does the amount supplied change as the price increases?

Question 80

Given the function f(x)=
find:
(a)the domain
(b)f(0)
(c)f(2)
(d)f(-2)
(e)f(-3)