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).
Step-by-step explanation:
Here, the given function is,
-----(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),
Thus, the x-intercept of h(x) is (4,0).
For slope, people sometimes use the description 'rise divided by run'. We know that the y axis describes rise, and the x axis describes run. So rise divided by run written numerically is . Now let's look at the line above. We can see that every time the y value goes up one unit, the x value goes right two units. This means that [tex]\frac{y}{x} --> \frac{y + 1}{x + 2}
This can be rewritten as 1/2, so the is 1/2. Hope this helped.