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3 years ago

Choose the function that represents the graph of the transformation of f(x) = |x| that opens down and has a vertex of (3,2)

Mathematics

2 answers:

dexar [7]3 years ago

8 0

f(x)=-|x-3|+2

Negative before the abs value inverts the graph and it moves right 3 and up 2

allsm [11]3 years ago

4 0

Answer:

f(x) = -|x - 3| + 2.

Step-by-step explanation:

f(x) = |x| is shaped like a V and the vertex is at (0, 0). f(x) = -|x| is a reflection in the x-axis so will be an inverted V , opening down. f(x) = - |x - 3| will be the -|x| moved 3 units to the right with the vertex at (3, 0). To bring the vertex to (3, 2) it will move upwards 2 units.

So it is f(x) = -|x - 3| + 2.

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algol [13]

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The origin does not lie in the region R, so we can ignore this point.

Now check the boundaries:

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Then

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Then

max{f (x, 0) | 1 ≤ x ≤ 4} = 21 when x = 4

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min{f(x, y) | 1 ≤ x ≤ 4, 0 ≤ y ≤ 2} = -11 at (x, y) = (4, 2)

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