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Calc 1 1.2

 

<== Calculus 1      Rules
Number Question Answer
See the work

1.

 

For the function ƒ(x) given in the graph


Match the following functions with their graphs.
Enter the letter of the graph below which corresponds       
to the function.

1. y=ƒ(x-2)

2. y=ƒ(-x)

3. y=2f(x)

4. y=ƒ(x)-2

 

1. D

2. C

3. B

4. A

The work

Point Cost: 3

2.

The graph of y=ƒ(x) is given below (in blue), along with
several related graphs (which are in red).

For each equation, enter the letter of the corresponding graph.          

1. y= -ƒ(x+4)

2. y= ƒ(x-4)

3. y= 2ƒ(x+6)

4. y= (1/3)ƒ(x)

5. y=ƒ(x)+3

 

1. B

2. A

3. D

4. E

5. C

The work

Point Cost: 3

3.

The graph of y=x^3-6x^2 is given below:

Find a formula for the transformation whose graph is given below

y=_______

 

y= -(x^3)+6*(x^2)+8              
The work

Point Cost: 2

4.

The graph of y=x^2 is given below:

Find a formula for each of the transformations whose graphs are
given below

a)

y=______

b)

y=______

 

a) y=(x-3)^2

b) x^2+3

The work

Point Cost: 2

5.

The graph of y=sqrt(x) is given below:

Find a formula for each of the transformations whose graphs are
given below

a)

y=______

b)

y=______

 

a) y=-sqrt(x)

b) y=sqrt(-x)

The work

Point Cost: 2

6.

The graph of y= |x| is given below:

Find a formula for each of the transformations whose graphs are
given below

a)

y= _______

b)

y=_______

 

a) y= 3|x|

b) y= -3|x|

 

 

The work

Point Cost: 3

7.

 

The graph of the function y=ƒ(x-20)+49 can be obtained from the           
graph of y=ƒ(x) by one of the following actions:


(a) shifting the graph of f (x) to the right 20 units
(b) shifting the graph of f (x) to the left 20 units
(c) vertically stretching the graph of f (x) by a factor 20
(d) vertically shrinking the graph of f (x) by a factor 20
Answer_______

Then, followed by one of the following actions:


(e) shifting the resulting graph upward 49 units
(f) shifting the resulting graph downward 49 units
(g) horizontally stretching the resulting graph by a factor 49
(h) horizontally shrinking the resulting graph by a factor 1/49
Answer______

 

A

E

The work

Point Cost: 1

8.

 

The graph of the function y = -42 f (x) can be obtained
from the graph of y = f (x) by one of the following actions:
(a) horizontally stretching the graph of f (x) by a factor 42
(b) horizontally shrinking the graph of f (x) by a factor 42
(c) vertically stretching the graph of f (x) by a factor 42
(d) vertically shrinking the graph of f (x) by a factor 42
Answer _____

Then followed by one of the following actions:

(e) reflecting the resulting graph in x-axis
(f) reflecting the resulting graph in y-axis
Answer _____

 

C

E

The work

Point Cost: 1

9.

 

Given that ƒ(x)=sqrt(1+x) and g(x)=sqrt(1-x), find formulas for the
following functions, and their domains. In each case, enter the domain using
interval notation.

 

 

a) sqrt(1+x)+sqrt(1-x)
    domain: [-1,1]

b) sqrt(1+x)-sqrt(1-x)
    domain: [-1, 1]

c) sqrt((1)^2-x^2)

    domain: [-1,1]

d) (sqrt(1+x))/(sqrt(1-x))
     domain: [-1,1)
The work

Point Cost: 4

10.

 

Given that ƒ(x)=x^2+4 and g(x)=x+5, calculate

 

 

 

 

 

 

a) (x+5)^2+4

    domain: (-∞, ∞)

b) x^2+(4+5)

    domain: (-∞, ∞)

c) (x^2+4)^2+4

    domain: (-∞, ∞)

d) x+10

    domain: (-∞, ∞)

 

 

The work

Point Cost: 4

11.

 

 

 

 

 

 

 

Given that ƒ(x)=1/x and  g(x)=3x+5, calculate

 

 

 

 

 

 

a) 1/(3x+5)

     domain≠ -5/3

b) (3/x)+5

    domain≠ 0

c) x

    domain≠ 0

d) 3(3x+5)+5

    domain: (-∞, ∞)

 

 

The work

Point Cost: 4

12.

 

Express the function h(x)=(x+9)^3 in the form ƒ o g. If ƒ(x)=x^3,
find the function g(x)

 

g(x)= x+9
The work

Point Cost: 3

13.

 

Express the function h(x)=1/(x+8) in the form ƒ o g. If g(x)=x+8,
find the function ƒ(x).

 

1/x
The work

Point Cost: 3

14.

For the function ƒ(x) and g(x) are given in the following graph

Find the corresponding function values

1. ƒ(g(3))

2. ƒ(g(2))

1. 2

2. 4

The work

Point Cost: 3