Respuesta :
Answer:
Step-by-step explanation:
is an increasing function as when the value of x increases the value of y increases
And when the value of x decreases , the value of y also decreases.
Now if we have (x+a) or (x-a) instead of x, the function shall have a horizontal shift.
So it shall either move left or right but shall not flip.
So
and
are increasing functions.
Only when x becomes -x, that the function shall flip & shall become a decreasing function.
But then it must be - (x-a) or -(x+a) inside.
So
is also increasing
Only
is a decreasing function.
Option D) is the right answer
The cube root is obtained by reversing the process of finding the cube of a
number, therefore, it can be negative.
- The cube root function that is always decreasing is; [tex]\underline{f(x) = \sqrt[3]{5 - x} }[/tex]
Reasons:
The given options;
f(x) = ∛(x - 8)
f(x) = ∛(x) - 5
[tex]f(x) = \sqrt[3]{5 - x}[/tex]
f(x) = ∛(x) + 5
Required: The cube root that is always decreasing as x increases.
Solution:
∛(x³) = x
Therefore, as x increases, x³ increases, and ∛(x³) = x increases
The analyzing the given options;
f(x) = ∛(x - 8)
In the above option, as x increases, (x - 8) increases, therefore, ∛(x - 8) increases
f(x) = ∛(x) - 5
In the above option, as x increases, ∛(x) increases, therefore, ∛(x) - 5 increases
- [tex]\underline{f(x) = \sqrt[3]{5 - x} }[/tex]
In the above option, as x increases, (5 - x) decreases, therefore, ∛(5 - x) decreases.
Therefore, the above cube root function is always decreasing as x increases
f(x) = ∛(x) + 5
In the above option, as x increases, ∛(x) increases, therefore, ∛(x) + 5 increases.
The cube root function that is always decreasing as x increases is option;[tex]\underline{f(x) = \sqrt[3]{5 - x} }[/tex]
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