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 7 units, the value of k is

k=7, g(x) = (0.5)x-7

Step-by-step explanation:

If g(x) is obtained by shifting down f(x) by 7 units, and f(x) passes through the origin (0,0) g(x) at the same instant passes through the same instant at  point (0,-7).

So f(x) =(2,1), (4,2),....

g(x) = (2,-6), ( 4,-5),....

And so on

Also, as K is the Linear if ti shifts down the line intercepts y-axis some units down. Since it is 7 units down for the y coordinate we can affirm g(x) =0.5 -k equals g(x)=0.5x -7

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.