Question

Which function is decreasing and approaches negative infinity as x increases? A. F(x) = 3(6)x ? 2 B. F(x) = -3(0.6)x + 1 C. F(x) = -3(6)x + 2 D. F(x) = 3(0.6)x ? 1

Answer 1

Answer:

Option C is correct.

$f(x)=-3(6)^{x+2}$

Explanation:

The exponential function is of the form:

$f(x) = ab^x$  where a is constant and b  is the base.

*If base b>1

(i) For positive value of a.

If x increases then, f(x) tends to positive infinity.

(ii)For negative value of a.

if x increases, then f(x) tends to negative infinity.

*if 0<b<1 ,

(i)For positive value of a.

If x increases then, f(x) tends to 0.

(ii)For negative value of a.

if x increases, then f(x) tends to 0.

Then from the given options

The only function $f(x)=-3(6)^{x+2}$ ; where a = -3 <0 and b=6>1 is decreasing and approaches negative infinity as x increases .