Question

The table shows three unique functions. (TABLE IN PIC) Which statements can be used to compare the characteristics of the functions? Select two options. f(x) has an all negative domain. g(x) has the greatest maximum value. All three functions share the same range. h(x) has a range of all negative numbers. All three functions share the same domain.

Answer 1

Answer:

Correct answers are:

g(x) has the maximum greatest value.

h(x) has a a range of all negative numbers.

Step-by-step explanation:

Let us learn about the domain and range of a function first.

Domain of a function is the input that we give to the function for which there is a valid output.

For example, let us consider a function:

$y=F(x) = x^2$

So, the value of 'x' that we provide to the function is known as the domain of function.

Range of a function is the output value when any input is given to the function.

For example,

$y=F(x) = x^2$

Let us put x = 4, which will be in the domain of function.

the output will be y = 16 which will be in the range of the function.

Now, let us consider the given functions f(x), g(x) and h(x).

Domain of f(x) i.e. the value of x for which the output is defined is:

{-2, -1, 1, 2}

Range of f(x) = $\{4, 4\frac{1}2, 5\frac{1}2, 6\}$

Max value of f(x) = 6

Domain of g(x) i.e. the value of x for which the output is defined is:

{-2, -1, 1, 2}

Range of g(x) = $\{6, 6\frac{1}2, 7\frac{1}2, 8\}$

Max value of g(x) = 8

Domain of h(x) i.e. the value of x for which the output is defined is:

{-2, -1, 1}

Range of h(x) = $\{-3, -2\frac{1}2, -1\frac{1}2\}$

Max value of h(x) = $-1\frac{1}2$

For x = 2, the value of h(x) is not given i.e. it is not defined at x = 2, so it is not in the domain. So, domain of all the three functions is not same.

So, the correct options are:

g(x) has the maximum greatest value.

h(x) has a a range of all negative numbers.