The graph of f(x) = |x| is transformed to g(x) = |x + 1| – 7. On which interval is the function decreasing?
2 answers:
Answer:
interval is the function decreasing.
Step-by-step explanation:
Given : The graph of is transformed to
To find : On which interval is the function decreasing?
Solution :
First we plot the graph of both the functions,
The graph of is shown with black line.
The graph of is shown with violet line.
Refer the attached figure below.
The graph shows the interval over which it is increasing or decreasing.
As we notice it is increasing on the interval
Decreasing on
Therefore, interval is the function decreasing.
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<h3>Answer: 6</h3>
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Explanation:
Rule: If a set has n elements in it, then it will have 2^n subsets.
For example, there are n = 3 elements in the set {a,b,c}. This means there are 2^n = 2^3 = 8 subsets. The eight subsets are listed below.
- {a,b,c} .... any set is a subset of itself
- {a,b}
- {a,c}
- {b,c}
- {a}
- {b}
- {c}
- { } ..... the empty set
Subsets 2 through 4 are subsets with exactly 2 elements. Subsets 5 through 7 are singletons (aka sets with 1 element). The last subset is the empty set which is a subset of any set. You could use the special symbol to indicate the empty set.
For more information, check out concepts relating to the power set.
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The problem is asking what value of n will make 2^n = 64 true.
You could guess-and-check your way to see that 2^n = 64 has the solution n = 6.
Another approach is to follow these steps.
Which is fairly trivial.
Or you can use logarithms to solve for the exponent.
Due to rounding error, we don't land exactly on 6 even though we should.