Identify the function that fits the description given below.
The six functions that are bounded below.
A. y=(x-1)^2 B.y=int(x+1) C. y= -sqrt(x)
D. y=x^3+1 E. y=2- (4/(1+e^-x)) F. y=-x
G. y = -sin x H. y= |x|-2 I. y= cos x+1
J. y=(x+2)^3 K. y= -1/x L. y= e^x-2
you need to find those that do not go off to -∞
So, start with
A: parabola that open up -- bounded below at the vertex
B: as x gets negative, so does y. so not B
check the others -- what do you think?
The function that fits the description of being bounded below is H. y = |x| - 2.
To determine if a function is bounded below, we need to assess whether there exists a lower limit for the values of y. In other words, we need to check if there is a y-value below which the function cannot go.
Looking at the provided functions, we can assess each one:
A. y = (x - 1)^2: This function is not bounded below as it can go to negative infinity.
B. y = int(x + 1): This function represents the greatest integer function, also known as the floor function. It is not bounded below as it can go to negative infinity.
C. y = -sqrt(x): This function is not bounded below as it can go to negative infinity.
D. y = x^3 + 1: This function is not bounded below as it can go to negative infinity.
E. y = 2 - (4 / (1 + e^-x)): This function is not bounded below as it can go to negative infinity.
F. y = -x: This function is not bounded below as it can go to negative infinity.
G. y = -sin(x): This function is not bounded below as it can go to negative infinity.
H. y = |x| - 2: This function is bounded below by -2 since the absolute value of x will always be non-negative, and subtracting 2 from it ensures the function cannot go below -2.
I. y = cos(x) + 1: This function is not bounded below as it can go to negative infinity.
J. y = (x + 2)^3: This function is not bounded below as it can go to negative infinity.
K. y = -1/x: This function is not bounded below as it can go to negative infinity.
L. y = e^x - 2: This function is not bounded below as it can go to negative infinity.
Therefore, the function that fits the description of being bounded below is H. y = |x| - 2.