Question

Consider the three functions below.

f(x) = -1 , g(x) = 4(1) , h(x) = -1(1)
Which statement is true?
a. The range of h(x) is y>0.
b. The domain of g(x) is y>0.
c. The ranges of f(x) and h(x) are different from the range of g(x).
d. The domains of f(x) and g(x) are different from the domain of h(x).

Answer 1

The ranges of f(x) and h(x) are different from the range of g(x).

Step-by-step explanation:

The three given functions are:

f(x) = -1

g(x) = 4(1)

h(x) = -1(1)

To determine the statement that is true, we can analyze each option:

1. The range of h(x) is y>0. Since h(x) is the product of -1 and 1, the range of h(x) is -1.
2. The domain of g(x) is y>0. Since g(x) is the product of 4 and 1, the range of g(x) is 4.
3. The ranges of f(x) and h(x) are different from the range of g(x). The range of f(x) is -1, the range of h(x) is -1, and the range of g(x) is 4. Therefore, this statement is true.
4. The domains of f(x) and g(x) are different from the domain of h(x). The domain of f(x) and g(x) is all real numbers, while the domain of h(x) is 1.

Therefore, the correct statement is c. The ranges of f(x) and h(x) are different from the range of g(x).