Question

Which function's range is the interval (-infinity,4]?
A. y = -(x-4)^2

B. R=3(x- 4)^2
C. y = [x] + 4
D..y = -5x + 4​

Answer 1

The y=-(x-4)^2

Then add the 20 + 10 and everything

Answer 2

Given:

A set of functions,

A. y = -(x-4)^2  

B. y=3(x- 4)^2

C. y = [x] + 4

D. y = -5x + 4.  

To Find:

The function whose range is (-infinity, 4].

Solution:

1. The function y = -(x-4)^2 has a minimum value of 0 and it is an increasing function. Hence the maximum value tends towards infinite. Hence the range is [0, infinite).

 

2. The function y = 3(x-4)^2 has a minimum value of 0 and it is an increasing function. Hence the maximum value tends towards infinite. Hence the range is [0, infinite).

3. y = [x] + 4 (where [x] = greatest integer function). This function is an increasing function with a minimum value towards negative infinity and the maximum value tends towards the positive side of infinity.  

=> Range of y = [x]  + 4 is (-infinite, infinite).

4. y = -5x+4 is a continuous increasing function without any exceptions.  

=> Range of y = -5x+4 is (-infinite,infinite)

Therefore, none of the functions has their range from (-infinity,4].