Graph each absolute value function.

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:

   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:

   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:

   Graph: see attachment 3

5=812a+9+3

step 1: simplify both sides of the equation.

5=812a+9+3

5=(812a)+(9+3)(combine like terms)

5=812a+12

5=812a+12

step 2: flip the equation.

812a+12=5

step 3: subtract 12 from both sides.

812a+12−12=5−12

812a=−7

step 4: divide both sides by 812.

812a /812 = -7/812

a= -1/116

so the answer is

a=   -1/116