Answer:
Options (1), (2), (3), (6)
Step-by-step explanation:
Given functions are,
f(x) = [tex]x^{\frac{1}{3} }[/tex]
h(x) = [tex](2x)^\frac{1}{3}+5[/tex]
Option (1)
y-intercept of function 'h',
x = 0,
h(x) = [tex](0)^\frac{1}{3}+5[/tex]
= 5
So y-intercept is (0, 5)
True.
Option (2)
Domain of function 'h' is (-∞, ∞)
True
Option (3)
As x approaches ∞, h(x) approaches ∞.
True.
Option (4)
For x intercept,
h(x) = 0
[tex](2x)^\frac{1}{3}+5=0[/tex]
2x = (-5)³
2x = -125
x = -62.5
So the x-intercept is (-62.5, 0)
False.
Option (5)
Range of the function 'h' is (-∞, ∞)
False
Option (6)
As x approaches to -∞, h(x) approaches to -∞.
Since, range of the function is (-∞, ∞), given statement is true.
Therefore, Options (1), (2), (3), (6) are correct.
