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Stels [109]
2 years ago
14

Tell whether the figure is a polygon. If it is a polygon,

Mathematics
1 answer:
elixir [45]2 years ago
5 0

Answers:

  • Polygon? <u>Yes</u>
  • Classify: <u>Pentagon</u>
  • The polygon is <u>concave</u>

===================================================

Explanation:

The figure is a polygon because it's composed of straight lines only, and we have a closed loop (or enclosed area).

This is a pentagon since it has 5 sides

The pentagon is concave because of the angle kicked in up top that caves in, so to speak. This interior angle exceeds 180 degrees and is known as a reflex angle.

Here's another way to determine the figure is concave: It's possible to pick two points inside the polygon such that the segment formed between them crosses outside the boundaries. See the diagram below.

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Identify the function that contains the data in the following table: x     -2         0         2         3         5     f(x)  
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{Since the definition of |x| is given by  

|x| = x, when x ≥ 0 and |x| = - x, when x < 0}

Again, the second  function gives the relation equation as f(x) = |x - 2|.

So, f(-2) = |-2 - 2| = |-4| = 4 ≠ 5

Now, the third function gives the relation equation as f(x) = |x - 2| - 1.

So, f(-2) = |-2 - 2| - 1 = |-4| - 1 = 4 - 1 = 3 ≠5

Again, the fourth function gives the relation equation as f(x) = |x - 2| + 1.

Hence, f(-2) = |-2 - 2| + 1 = |-4| + 1 = 4 + 1 = 5  

Therefore, the fourth function f(x) = |x - 2| + 1 contains the given data table.  

For further clarity we can check f(0) = 3, f(2) = 1, f(3) = 2 and f(5) = 4. (Answer)

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