ANSWER
Yes,
![x > 5](https://tex.z-dn.net/?f=x%20%3E%205)
is the restriction.
EXPLANATION
The given function is
![f(x) = log(x - 5) + 1](https://tex.z-dn.net/?f=f%28x%29%20%3D%20log%28x%20-%205%29%20%2B%201)
This is a logarithmic function that is defined for
![x - 5 > 0](https://tex.z-dn.net/?f=x%20-%205%20%3E%200)
The reason is that, the logarithmic functions are not defined for negative values of x and 0.
Therefore the argument must always be positive.
When we solve the above inequality, we get,
![x > 5](https://tex.z-dn.net/?f=x%20%3E%205)
Therefore the the restrictions is that,
![x > 5](https://tex.z-dn.net/?f=x%20%3E%205)
This is also the same as the domain of the function.
Answer:
At each vertex at least 3 faces meet (maybe more).
Step-by-step explanation:
Answer:
(0,4) vertex and (1,3) another pt
Step-by-step explanation:
The parabola has been shifted up 4 units from parent function (there is also a reflection)...but we only really care about the shift 4 units up from (0,0) for our vertex... Our vertex is (0,4)
Now just plug in another number to find another point...let's do x=1
Plug in you get -1^2+4=-1+4=3 so another point is (1,3)
Answer:
The y-intercept is (0,210)
Step-by-step explanation:
We have the function, ![f(x)=201+9e^{3x}](https://tex.z-dn.net/?f=f%28x%29%3D201%2B9e%5E%7B3x%7D)
So, we know that,
<em>'y-intercept is the point on the graph where the function crosses y-axis'.</em>
i.e. y-intercept is obtained when x=0.
Thus, substituting x=0 in the given function, we get,
![f(0)=201+9e^{3\times 0}](https://tex.z-dn.net/?f=f%280%29%3D201%2B9e%5E%7B3%5Ctimes%200%7D)
i.e. ![f(0)=201+9e^{0}](https://tex.z-dn.net/?f=f%280%29%3D201%2B9e%5E%7B0%7D)
i.e. ![f(0)=201+9\times 1](https://tex.z-dn.net/?f=f%280%29%3D201%2B9%5Ctimes%201)
i.e. ![f(0)=201+9](https://tex.z-dn.net/?f=f%280%29%3D201%2B9)
i.e. f(0) = 210
Also, we can see from the given graph that the function crosses y-axis at (0,210).
Hence, the y-intercept is (0,210).
Answer:
A. 36
Step-by-step explanation:
A composite number is a number that can be divided evenly by more numbers than 1 and itself. It is the opposite of a prime number. The number 36 can be evenly divided by 1, 2, 3, 4, 6, 9, 12, 18 and 36, with no remainder. Since 36 cannot be divided by just 1 and 36, it is a composite number.