Question

How does the graph of g(x) = x – 3 compare with the graph of the parent function, f(x) = x? A. The graph of g(x) is compressed horizontally by a factor of 3. B. The graph of g(x) is compressed vertically by a factor of 3. C. The graph of g(x) is shifted 3 units to the left. D. The graph of g(x) is shifted 3 units down.

Answer 1

g(x) = x - 3

The - 3 in this question will move the graph down by 3.

Compare the points made by f(x) and g(x)

f(x)
(0,0);(1,1);(2,2)

g(x)
(0,-3);(1,-2);(2,-1)

Therefore, the answer is D.

Answer 2

Answer with explanation:

Parent Function

 f(x)=x

→y=x

Image of Parent Function

 g(x)= x -3

→y=x-3

When you will look at the graph of parent function , it passes through , (0,0) and from first and fourth Quadrant.

And when you will look at the graph of , Image , you will see that, it cuts ,X axis at , (3,0) and y axis at , (0,-3).

So, you can say that , function g(x) is either shifted 3 units to left or 3 units down.

Option D: →The graph of g(x) is shifted 3 units down.