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When f(x) = -|x| is graphed on a regular coordinate grid, the graph forms a(n) _____ angle at its vertex.

a. acute
b. right
c. obtuse

1 Answer

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Final answer:

The graph of f(x) = -|x| forms a right angle at its vertex. It is a V-shaped graph that opens vertically downward with two lines meeting at a 90-degree angle at the origin.

Step-by-step explanation:

When f(x) = -|x| is graphed on a regular coordinate grid, the graph forms a right angle at its vertex. The function f(x) = -|x| creates a V-shaped graph that opens vertically downward in the coordinate system, with the vertex at the origin (0,0). This V-shape has two linear pieces, one with a positive slope and one with a negative slope, that meet at the vertex. Looking closely at the vertex where these two lines meet, it is clear that they form a 90-degree angle, also known as a right angle. This is because the absolute value function, represented as |x|, is always non-negative, resulting in a graph that is symmetrical about the y-axis and has two opposite, identical sloped lines reflecting each other across the y-axis.

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