Question pt. 2 how would you do this problem if the numbers don't cancel each other out.
1 answer:
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Given:
The graph of a function.
To find:
The domain and range of the function.
Solution:
We have, the graph of a function and we need to find the domain and range of the function.
We know that, domain is the set of input values (x-values) and range is the set of output values (y-values).
From the given graph it is clear that function is defined for all values of x except x=0 because as x tends to 0 the function tends to negative or positive infinite. So, domain can be any real number except 0.
From the given graph it is clear that the value of function can be any real number except y=0. So, range can be any real number except 0.
Therefore, the correct option is B.
9514 1404 393
Answer:
- vertical shift: 7 (up)
- horizontal shift: 2 (right)
- vertical asymptote: x=2
- domain: x > 2
- range: all real numbers
Step-by-step explanation:
For any function f(x), the transformation f(x -h) +k represents a horizontal shift of h units to the right and k units upward.
Here, the parent function is log₂(x) and the transformation to log₂(x -2) +7 represents translation 2 units right and 7 units upward.
The parent function has a vertical asymptote at x=0, so the shifted function will have a vertical asymptote at x-2=0, or x = 2.
The parent function has a domain of x > 0, so the shifted function will have a domain of x-2 > 0, or x > 2.
The parent function has a range of "all real numbers." Shifting the function vertically does not change that range. The range of the shifted function is still "all real numbers."
The graph is shown below. The vertical asymptote is the dashed orange line.
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The "work" is in matching the pattern f(x -h) +k to the function log₂(x -2) +7.
