The smallest number is 1 and the largest number is 8. The range is the largest minus the smallest, so it is 8-1=7.
What is the range of function of y= 9x
Yes. Typical example: y = x2. To avoid comparing infinite sets, restrict the function to integers between -3 and +3. Domain = -3, -2 , ... , 2 , 3. So |Domain| = 7 Range = 0, 1, 4, 9 so |Range| = 4 You have a function that is many-to-one. One consequence is that, without redefining its domain, the function cannot have an inverse.
In Excel you can use the SMALL() function The small function can retrieve the smallest values from data based on rank. For example: =SMALL(range,1) // smallest =SMALL(range,2) // 2nd smallest =SMALL(range,3) // 3rd smallest
3,3,4,2,1,3,3 3-3=0 range=0
The range ot 2, 1, 3, 4, 4, and 4 is 3.
That depends on the specific function.
x y -3 2 -1 6 1 -2 3 5
What is the range of function of y= 9x
the range for 5 2 1 and 3 is 4.
mean= 2, mode= 1 and 3, median= 3, and range= 2
Maybe; the range of the original function is given, correct? If so, then calculate the range of the inverse function by using the original functions range in the original function. Those calculated extreme values are the range of the inverse function. Suppose: f(x) = x^3, with range of -3 to +3. f(-3) = -27 f(3) = 27. Let the inverse function of f(x) = g(y); therefore g(y) = y^(1/3). The range of f(y) is -27 to 27. If true, then f(x) = f(g(y)) = f(y^(1/3)) = (y^(1/3))^3 = y g(y) = g(f(x)) = g(x^3) = (x^3)^3 = x Try by substituting the ranges into the equations, if the proofs hold, then the answer is true for the function and the range that you are testing. Sometimes, however, it can be false. Look at a transcendental function.
Yes. Typical example: y = x2. To avoid comparing infinite sets, restrict the function to integers between -3 and +3. Domain = -3, -2 , ... , 2 , 3. So |Domain| = 7 Range = 0, 1, 4, 9 so |Range| = 4 You have a function that is many-to-one. One consequence is that, without redefining its domain, the function cannot have an inverse.
f(x) = 2 cos 3x The amplitude: A = |2| = 2 The maximum value of the function: 2 The minimum value of the function: -2 The range: [-2, 2]
In Excel you can use the SMALL() function The small function can retrieve the smallest values from data based on rank. For example: =SMALL(range,1) // smallest =SMALL(range,2) // 2nd smallest =SMALL(range,3) // 3rd smallest
{(-2,0),(-4,-3),(2,-9),(0,5),(-5,7)}
3,3,4,2,1,3,3 3-3=0 range=0
The range ot 2, 1, 3, 4, 4, and 4 is 3.