Answer:
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
