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
8/5 is rational. It is expressed as a ratio of two integers.
√4 = 2 = 2/1 . This is rational because it expressed as ratio of two integers.
√64 = 8. This is rational because it expressed as ratio of two integers.
√10 = 3.16227..... The decimal part does not end and it is irrational because it can not be expressed as ratio of two integers.
Therefore √10 is irrational.
Answer:
42
Step-by-step explanation:
Yes, you are right.
6 weeks * 7 days in a week.
so 7 days in all 6 weeks is 42 days.
Answer:
(-2, 4)
Step-by-step explanation:
~When reflecting a point of the x-axis, the x value (or first number inside the parenthesis) does not change.
The reason the x-value does not change is because you are reflecting over the x-axis, making the point go up or down. That will change the y-value but the x-value only changes if you move to the left or the right. In this case, you can see that the point's x-value is -2, so that will not change. It's current y-value however is -4. When reflecting over an axis, the number that is changing (in this case the y-value) will just be flipped from positive to negative, or vise versa. In this case, -4 will be reflected to be 4, making point C reflected over the x-axis (-2, 4).
Answer:
= 0.857143 miles per hour
Step-by-step explanation:
This the fractions 3/4 miles and 7/8 hours are equal to
0.75 miles and 0.875 hours
We want a unit rate where
1 is in the denominator,
so we divide top and bottom by 0.875
<u>0.75 miles</u> ÷ 0.875
0.875 hours ÷ 0.875
=
<u>0.857143 miles</u>
1 hour
so the answer would be...
= 0.857143 miles per hour
