Question

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

Answer 1

Answer:

I would choose B

Step-by-step 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

Answer:

The correct options are B, C and D.

Step-by-step 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 | -∞ < 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,

$f(3)=-\sqrt[3]{3}\neq -27$

Option E is correct.

Therefore the correct options are B, C and D.