Question

Which statement is true of the function f(x) = -3^sqrt x ? Select three options.

Answer 1

Answer:

b,c,d

Step-by-step explanation:

Just took the test

Answer 2

Do you mean $f(x)=-3^{\sqrt x}$, as in the negative of 3 to the power of √x ? Or $f(x)=-\sqrt[3]{x}$, as in the negative cube root of x ?

If you mean $f(x)=-3^{\sqrt x}$, then, going through each option:

• no: the square root component is defined only for x ≥ 0, for which we have √x ≥ 0 and hence f(x) < 0 for all x in the domain. √x is an increasing function, so the powers of 3 get successively larger, so f(x) would be always decreasing;

• no: as mentioned above, the domain would be all non-negative numbers;

• no: at minimum, x = 0 which gives f (0) = -3⁰ = -1, and because f(x) is decreasing over its entire domain, the range would be {y | y ≤ -1};

• no: again, a bit of ambiguity, but assuming you mean to say here $y=3^{\sqrt x}$, yes, f(x) would be a reflection of y across the x-axis;

• and finally, no: $f(3)=-3^{\sqrt3}\approx-6.705$

so that only the fourth option would be true.

On the other hand, if you mean $f(x)=-\sqrt[3]{x}$, then:

• no: the function is always decreasing;

• yes: the domain is all real numbers;

• yes: the range is {y | -∞ < y < ∞};

• yes: f(x) is a reflection of y=∛x, also about the x-axis; and

• no: f (3) = -∛3 ≈ -1.442

I suspect you mean the second case, since it's a bit simpler to approach.