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

question 45

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

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Definitions:

Margin of Error

The maximum expected difference between the true population parameter and a sample estimate of that parameter.

Mean

The average of a set of numbers, calculated by adding all the values together and dividing by the number of values.

T Distribution

A probability distribution used in statistical analysis that compares sample data to the standard normal distribution, especially useful when the sample size is small.

Population Standard Deviation

The standard deviation of a set of values that includes an entire population.