Which of the following could be an example of a function with a domain [a,∞) and a range (-∞,b] where a > 0 and b > 0?

a)f(x)= √x+a -b

b) f(x)= -√x-a +b

c)f(x)= 3√x+a -b

d) f(x)= ^3√(x-b) +a

Step-by-step explanation:

We are given a few functions in options and we have to choose from them that has the domain [a,∞) and range (-∞,b].

Now, for domain i.e. the value of x ≥ a.

Therefore, the value of y must be a function of

So, there is only one function ............ (1), that has  the term in it.

Now, for x = a, the value of f(x) becomes b and for x = ∞ the function f(x) value becomes -∞.

Therefore, the range of the function will be (-∞,b] i.e. y ≤ b.  

Hence, the required function is . (Answer)

47

step-by-step explanation:

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0