Question

Which statement is true of the function f(x) = -³√x

A. The function is always increasing
B. The function has a domain of all real numbers
C. The function has a range of {y}- infinity D. The function is a reflection of y=³√x
E. The function passed through the point (3,-27)

100 point!!!!

Answer 1

I would choose B

Explanation:

f(x) = - (x) ^ (1/3)

A. The function is always increasing

This decreases as x gets larger

B. The function has a domain of all real numbers

This is true, x can be any number as long as we assume a real valued root instead of the principle root

C. The function has a range of {y}- infinity

The range is all real numbers

D. The function is a reflection of y=³√x

y = -³√x is a reflection across the x axis, this just says reflection. Which reflection, the x axis, the y axis or y=x?

E. The function passed through the point (3,-27)

y = - (3)^ 1/3 which is -1.44224957

Answer 2

The correct options are B, C and D.

Explanation:

The given function is

`f(x)=-\sqrt[3]{x}`

Using graphing calculator draw the graph of given function.

From the given graph it is clear that:

1. The function is always decreasing. Option A is incorrect.

2. The function is defined for all values of x. So, domain of the function is all real numbers. Option B is correct.

3.
`f(x)\rightarrow \infty \text{ as }x\rightarrow -\infty`

`f(x)\rightarrow -\infty \text{ as }x\rightarrow \infty`

The output value of the function can be all real number. So, range of the function is all real number.

Range = -∞ < y < ∞

Option C is correct.

4. If f(x)=-g(x) then f(x) and g(x) are reflection of each other along x axis.

The given function is a reflection of y=³√x. Option D is correct.

5. At x=3,

`f(3)=-\sqrt[3]{3}\\eq -27`

Option E is correct.

Therefore the correct options are B, C and D.