NOTES: y = a|x - h| + k
Vertex = (h, k)
AOS: x = h
Domain: x = All Real Numbers (-∞, ∞)
Range: if "a" is positive → y ≥ k
if "a" is negative → y ≤ k
Comparison to Parent Function: "a" is vertical stretch
"h" is horizontal shift (left, right)
"k" is vertical shift (up, down)
Graph: Plot the vertex
Plot a point to the right by counting rise over run using the "a"-value
Plot a point to the left by counting rise over run using opposite of "a"-value
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4. f(x) = 3|x - 5| + 2
a = 3 h = 5 k = 2
Vertex: (5, 2) AOS: x = 3
Domain: x = ARN (-∞, ∞) Range: y ≥ 2
Comparison to Parent Function:
vertical stretch by a factor of 3horizontal shift 5 units to the rightvertical shift 2 units up
Graph: see attachment 1
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a = h = -4 k = -3
Vertex: (-4, -3) AOS: x = -4
Domain: x = ARN (-∞, ∞) Range: y ≤ -3
Comparison to Parent Function:
reflection over the x-axisvertical shrink by a factor of 1/2horizontal shift 4 units to the leftvertical shift 3 units down
Graph: see attachment 2
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6. f(x) = -4|x - 3|
a = -4 h = 3 k = 0
Vertex: (3, 0) AOS: x = 3
Domain: x = ARN (-∞, ∞) Range: y ≤ 0
Comparison to Parent Function:
reflection over the x-axisvertical stretch by a factor of 4horizontal shift 3 units to the right
Graph: see attachment 3