Question

How does the graph of g(x)=⌊x⌋−3 differ from the graph of f(x)=⌊x⌋? The graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted right 3 units. The graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted up 3 units. The graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted down 3 units. The graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted left 3 units.

Answer 1

The graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted down 3 units

Explanation:

f(x)=⌊x⌋ is the parent function

g(x)=⌊x⌋ - 3 = f(x) - 3, that is, the parent function subtracted by 3

This subtraction shifted down (3 units in this case) the parent function.

Answer 2

The graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted down 3 units.

Explanation:

g(x) = ⌊x⌋−3 = f(x) -3

When we add or subtract from the function, this is a shift up or down

Since we are subtracting this is a shift down of 3