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Jet001 [13]
3 years ago
10

Let |x| + |y| = c where, c is s real number. Determine the number of points that would be on the graph of the equation for each

given cases:
Case 1: c < 0
Case 2: c = 0
Case 3: c > 0

Mathematics
1 answer:
IRINA_888 [86]3 years ago
8 0

Answer:

  1. 0
  2. 1
  3. an infinite number

Step-by-step explanation:

<u>Case 1</u>

The absolute value of a number will not be negative, so the function is the sum of two non-negative numbers. That sum cannot be negative, so there will be no points on the graph.

<u>Case 2</u>

The sum of two non-negative numbers can be zero if they both are zero. This graph will have exactly one point: (x, y) = (0, 0). (In the attached, it doesn't show up.)

<u>Case 3</u>

There are an infinite number of ways two non-negative numbers can sum to a positive number. There will be an infinite number of points on the graph. The line segments in the attached graph illustrate that for c = 1.

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<h3>How to determine a piecewise function</h3>

In this question we have a graph formed by two different <em>linear</em> functions. <em>Linear</em> functions are polynomials with grade 1 and which are described by the following formula:

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f(x) = \left \{ {{-0.5\cdot x +1, \,x < 0} \atop {2\cdot x - 2, \,x \ge 0}} \right.

Based on the characteristics of <em>linear</em> and <em>piecewise</em> functions, the <em>piecewise</em> function f(x) = \left \{ {{-0.5\cdot x +1, \,x < 0} \atop {2\cdot x - 2, \,x \ge 0}} \right. is shown in the graph attached herein. (Correct choice: A)

To learn more on piecewise functions: brainly.com/question/12561612

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