Determine Algebraically Whether the Following Function Is One-To-One $$| x - 5 | , \quad x \leq 5$$

question 9

Multiple Choice

Determine algebraically whether the following function is one-to-one.
$$| x - 5 | , \quad x \leq 5$$

• A)
• \[\begin{aligned}
• | a - 5 | & = | b - 5 | \\
• 5 - a & = 5 - b \quad ; \text { one-to-one } \\
• - a & = - b \quad \\
• a & = b
• \end{aligned}\]
• B)
• \[\begin{aligned}
• | a - 5 | & = | b - 5 | \\
• | a | - 5 & = | b | - 5 \\
• | a | & = | b | \\
• a & = b
• \end{aligned}\]
• C)
• \[\begin{aligned}
• | a - 5 | & = | b - 5 | \\
• a + 5 & = 5 - b \quad ; \text { not one-to-one } \\
• a & = - b
• \end{aligned}\]
• D)
• \[\begin{aligned}
• | a - 5 | & = | b - 5 | \\
• | - 5 | - a & = | - 5 | + b ; \text { not one-to-one } \\
• - a & = b
• \end{aligned}\]
• E)
• \[\begin{aligned}
• | a - 5 | & = | b - 5 | \\
• | - 5 | - a & = | - 5 | - b \\
• - a & = - b \\
• a & = b
• \end{aligned}\]

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Definitions:

Sexually Selected Ornaments

Physical traits evolved through sexual selection, often used to attract mates or compete with members of the same species, such as the colorful plumage of many birds.

Female Choice

A form of sexual selection where females choose their mates, often based on traits that indicate the male's genetic quality or fitness.

Cost of Sexual Reproduction

The energy and resources expended by organisms to produce offspring through sexual means, as opposed to asexual reproduction, which often incurs less cost.

Recombinant Chromosomes

Chromosomes that are formed by crossing over and recombination between homologous chromosomes during meiosis, resulting in new combinations of genetic material.