Answer:
Here we have the domain:
D = 0 < x < 1
And we want to find the range in that domain for:
1) y = f(x) = x
First, if the function is only increasing in the domain (like in this case) the minimum value in the range will match with the minimum in the domain (and the same for the maximums)
f(0) = 0 is the minimum in the range.
f(1) = 1 is the maximum in the range.
The range is:
0 < y < 1.
2) y = f(x) = 1/x.
In this case the function is strictly decreasing in the domain, then the minimum in the domain coincides with the maximum in the range, and the maximum in the domain coincides with the minimum in the range.
f(0) = 1/0 ---> ∞
f(1) = 1/1
Then the range is:
1 < x.
Notice that we do not have an upper bound.
3) y = f(x) = x^2
This function is strictly increasing, then:
f(0) = 0^2 = 0
f(1) = 1^2 = 1
the range is:
0 < y < 1
4) y = f(x) = x^3
This function is strictly increasing in the interval, then:
f(0) = 0^3 = 0
f(1) = 1^3 = 1
the range is:
0 < y < 1.
5) y = f(x) = √x
This function is well defined in the positive reals, and is strictly increasing in our domain, then:
f(0) = √0 = 0
f(1) = √1 =1
The range is:
0 < y < 1
Answer:
=
Step-by-step explanation:
Answer:
Step-by-step explanation:
The standard equation of a hyperbola is given by:
where (h, k) is the center, the vertex is at (h ± a, k), the foci is at (h ± c, k) and c² = a² + b²
Since the hyperbola is centered at the origin, hence (h, k) = (0, 0)
The vertices is (h ± a, k) = (±√61, 0). Therefore a = √61
The foci is (h ± c, k) = (±√98, 0). Therefore c = √98
Hence:
c² = a² + b²
(√98)² = (√61)² + b²
98 = 61 + b²
b² = 37
b = √37
Hence the equation of the hyperbola is:
Answer:
d. vertical line
Step-by-step explanation:
A line with an undefined slope is a vertical line
Slope is the change in y over the change in x
When the slope is undefined, it means that the x does not change, which is a vertical line
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