The equation of vertical shift is g(x) = 2x + 3.
They are parallel, no intersect.
How to translate a function.
Locate two points on the graph of f
Consider (-2,-4) and (2,4)
slope= y₂ - y₁/x₂ - x₁
m = 4 - (-4)/2 - (-2)
m = 8/4 = 2
Since the graph passes through the origin (0,0), it has no y-intercept.
General equation of a line is
y = mx + b
where
m is slope
b is y-intercept
m = 2
b = 0
So, equation of the line is f(x) = 2x.
For horizontal translation, use g(x) = 2(x - h
where
h is the amount of horizontal shift.
For a vertical translation, use g(x) = 2x + k
where
k is the amount of vertical shift.
Let's consider the vertical shift
Since g(x) is a linear function, it will intersect with f(x) = 2x unless it's a parallel shift.
If k is zero, meaning no vertical shift, the graphs will coincide.
For example, vertical translation upward by 3 units.
f(x) = 2x
g(x) = 2x + 3
Since f(x) and g(x) have same slope they will parallel to each other and no intersection.