Question

The graph of f(x) = (0.5)^x is replaced by the graph of g(x) = (0.5)^x - k. If g(x) is obtained by shifting f(x) down by 3 units, the value of k is?

Answer 1

Step-by-step explanation:

Consider the following parental function f(x):

`f(x)=0.5^x`

Now, according to the problem, the graph of this function is replaced by the graph of g(x) which is defined as a follows:

`g(x)=0.5^x\text{ - k}`

Notice that the transformation that was applied to the function f(x) is a vertical shift of the graph. If k>0, by definition, the vertical shifts of the graphs are:

1) To graph y = f(x) + k, shift the graph of y=f(x) upward k units.

2) To graph y = f(x) - k, shift the graph of y=f(x) downward k units.

According to the second definition, if g(x) is obtained by shifting f(x) down by 3 units, the value of k would be 3 and we obtain:

`g(x)=0.5^x\text{ - 3}`

we can conclude that the correct answer is:

Answer:

`k\text{ = 3}`