What is the sum of -6 and 9
1 answer:
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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.
Answer:
Step-by-step explanation:
Here, we assume that point A is (-1, 0) and point B is (z, 2). Since angle BAD is 60°, we have ...
2/(z+1) = tan(60°) = √3
z = (2/√3) -1
Putting the value of z into the equation for the parabola lets us find "a".
2 = a(z +1)(z -5) = a(2/√3)(2/√3 -6)
Then ...
a = 2/(4/3 -12/√3) = (6√3)/(4√3 -36)
a = -(3+9√3)/52 ≈ −0.357470332079
Answer:
The system of inequalities is equal to
Step-by-step explanation:
Let
x-----> the number of hours that Malik works at a hardware store
y-----> the number of hours that Malik works as a lifeguard
we know that
-----> inequality A
-----> inequality B
Using a graphing tool
The solution is the shaded area
see the attached figure
