Asa
match each graph with the logarithmic function it represents.

f(x)=3-4 In (x-2)=graph 3

f(x)=3-In x=graph 1

f(x)=In (x+1)=graph 4

f(x)= 2In (x+3)= graph 2

Step-by-step explanation:

Use a graph tool to visualize the functions.Attached are the graphed functions respectively.

f(x) = 3 - 4㏑(x - 2) ⇒ graph 3

f(x) = 3 - ㏑(x) ⇒ graph 1

f(x) = ㏑(x + 1) ⇒ graph 4

f(x) = 2㏑(x + 3) ⇒ graph 2

Step-by-step explanation:

* Lets look to the graphs and solve the problem

- We will use some points on each graph and substitute in the function

  to find the graph of each function

- Remember: ㏑(1) = 0 and ㏑(0) is undefined

- Lets solve the problem

# f(x) = 3 - 4㏑(x - 2)

- Let x - 2 = 1 because ㏑(1) = 0, then f(x) will equal 3

∵ x - 2 = 1 ⇒ add 2 for both sides

∴ x = 3

- Substitute the value of x in f(x)

∴ f(x) = 3 - 4㏑(3 - 2)

∴ f(x) = 3 - 4㏑(1) ⇒ ㏑(1) = 0

∴ f(x) = 3

∴ Point (3 , 3) lies on the graph

- Look to the graphs and find which one has point (3 , 3)

∵ Graph 3 has the point (3 , 3)

∴ f(x) = 3 - 4㏑(x - 2) ⇒ graph 3

# f(x) = 3 - ㏑(x)

- Let x = 1 because ㏑(1) = 0, then f(x) will equal 3

- Substitute the value of x in f(x)

∴ f(x) = 3 - ㏑(1) ⇒ ㏑(1) = 0

∴ f(x) = 3

∴ Point (1 , 3) lies on the graph

- Look to the graphs and find which one has point (1 , 3)

∵ Graph 1 has the point (1 , 3)

∴ f(x) = 3 - ㏑(x) ⇒ graph 1

# f(x) = ㏑(x + 1)

- Let x = 0 because ㏑(1) = 0, then f(x) will equal 0

- Substitute the value of x in f(x)

∴ f(x) = ㏑(0 + 1) = ㏑(1) ⇒ ㏑(1) = 0

∴ f(x) = 0

∴ Point (0 , 0) lies on the graph

- Look to the graphs and find which one has point (0 , 0)

∵ Graph 4 has the point (0 , 0)

∴ f(x) = ㏑(x + 1) ⇒ graph 4

# f(x) = 2㏑(x + 3)

- Let x + 3 = 1 because ㏑(1) = 0, then f(x) will equal 0

∵ x + 3 = 1 ⇒ subtract 3 from both sides

∴ x = -2

- Substitute the value of x in f(x)

∴ f(x) = 2㏑(-2 + 3) = 2㏑(1) ⇒ ㏑(1) = 0

∴ f(x) = 0

∴ Point (-2 , 0) lies on the graph

- Look to the graphs and find which one has point (-2 , 0)

∵ Graph 2 has the point (-2 , 0)

∴ f(x) = 2㏑(x + 3) ⇒ graph 2

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2