2-6 Vertical and Horizontal Translations
Concept #1 Comparing Graphs
Translation - An operation that shifts a graph both horizontally, vertically, or
both.
Ex. 1 Compare the graphs of y = x with y = x - 3
Ex. 2 Compare the graphs of f(x) = - lxl with f(x) = - lxl + 2
Concept # 2 Graphing a Vertical Translation
Translation
Parent Function
y = x + k(shifts k units up)
y=x
y = x - k(shifts k units down)
y = lxl + k(shifts k units up)
y = lxl
y = lxl - k(shifts k units down)
Ex. 4 Graph y = -lxl + 3
Ex. 3 Graph y = x - 2
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Concept #3 Writing Equations for Vertical Translations
Ex. 6 y = l3xl, 5 units up
Ex 5. y = 2x, 4 units down
Concept #4 Graphing Horizontal Translations
y = lx + kl(shifts k units left)
y = lxl
y = lx - kl(shifts k units right)
Ex 7. Graph y = lx + 3l
Ex. 8 Graph y = -lx - 2l
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Concept #5 Writing Equations for Horizontal Translations
Use y = lxl as the parent function
Ex. 9
Ex. 10
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Concept #6 Graphing Diagonal Translations
Ex. 12 y = -lx + 2l - 4
Ex. 11 y = lx - 3l + 1
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Oct 2­7:39 AM
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