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write and graph a function g that is a horizontal or vertical translation of the graph of f . do the graphs ever intersect ?

User Frodnar
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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.

write and graph a function g that is a horizontal or vertical translation of the graph-example-1
write and graph a function g that is a horizontal or vertical translation of the graph-example-2
User Zheng Zhongqi
by
7.2k points

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