Question

Let f(x)=-4(2)^x. The graph of g(x)=f(x)+k is shown below. Identify the value of k.

Answer 1

Given:

The function is:

$f(x)=-4(2)^x$

The graph of the function $g(x)=f(x)+k$ is given.

To find:

The value of k.

Solution:

We have,

$f(x)=-4(2)^x$

$g(x)=f(x)+k$

Using these two functions, we get

$g(x)=-4(2)^x+k$

From the given graph it is clear that the graph of g(x) passes through the point (0,2). It means the point (0,2) satisfies the function g(x).

Substituting $g(x)=2$ and $x=0$ in the above function, we get

$2=-4(2)^0+k$

$2=-4(1)+k$

$2=-4+k$

$2+4=k$

$6=k$

Therefore, the value of k is 6.