Question

Which statements are true of the graph of h(x) = ^3 square root of x-4 ? Check all that apply.

The domain of h(x) is the set of all real numbers.

The range of h(x) is the set of all real numbers.

For all points (x, h(x)), h(x) exists if and only if x – 4 0.

The graph of h(x) is a translation of f(x) down 4 units.

The graph of h(x) intercepts the x-axis at (4, 0).

Answer 1

A,B,E

Explanation:

Answer 2

Answer: The true statements are,

The domain of h(x) is the set of all real numbers.

The range of h(x) is the set of all real numbers.

The graph of h(x) intercepts the x-axis at (4, 0).

Explanation:

Here, the given function is,

`h(x) =\sqrt[3]{x-4}` -----(1)

Which is cubic root function,

Since, a cubic function can be written as ∛p(x), where p(x) is a polynomial,

We know that,

The all possible value of x in the polynomial p(x) = Set of all real numbers

⇒ The domain of a polynomial = Set of real all numbers

⇒ The domain of a cubic function = Set of real all numbers

Hence, the domain of given function h(x) = Set of all real numbers,

Similarly, the range of a polynomial is also the set of real numbers,

⇒ The range of given function h(x) = Set of all real numbers,

Now, for x-intercept, y = 0 or h(x) = 0,

From equation (1),

`0 =\sqrt[3]{x-4}`

`\implies x-4=0\implies x = 4`

Thus, the x-intercept of h(x) is (4,0).