Question

Which graph models the function f(x) = -4(2)x?

Answer 1

It is C. 

If you type in your calculator "Y=" and then " -4(2)^x " and click "GRAPH" you will see a descending graph, from left to right, that looks EXACTLY like the third graph in option C. 

Answer 2

Answer:

Option C is correct.

Step-by-step explanation:

The exponential function is of the form: $f(x) = ab^x$

 where a is initial value 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.

Given the exponential function $f(x) = -4(2)^x$

Here, value of a = -4 and b = 2>1

From the above definition,

as we increase x$\rightarrow +\infty$ , f(x)$\rightarrow -\infty$.

Y-intercept ( plug x =0 to solve for y)

Substitute the value of x =0 in given equation;

$y =-4(2)^0 = -4 \cdot 1 = -4$

Y-intercept (0, -4)

Therefore, the only correct option is C because if we increase the value of x,  the function f(x) tends to negative infinity and also it cut the y-axis at y = -4.