Match the Graph with Its Function Using the X-Intercepts $y _ { 1 } = 5 ( 4 x - 1 ) ^ { - 1 } , y _ { 2 } = 2 ( 4 x - 1 ) ^ { - 2 }$

question 370

Multiple Choice

Match the graph with its function using the x-intercepts.
- $y _ { 1 } = 5 ( 4 x - 1 ) ^ { - 1 } , y _ { 2 } = 2 ( 4 x - 1 ) ^ { - 2 }$ , and $y _ { 1 }$ exceeds $y _ { 2 }$ by 2

• A) \(\frac { 3 } { 4 } , \frac { 3 } { 8 }\)
• B) \(- 2 , - \frac { 1 } { 2 }\)
• C) \(- \frac { 1 } { 4 } , 0\)
• D) \(- \frac { 1 } { 4 } , - \frac { 1 } { 8 }\)

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Definitions:

Random Variable

A variable that assumes numerical outcomes as a result of random events.

Constant

A value that remains unchanged throughout the execution of a process or formula.

Poisson Random Variable

A random variable that represents the number of events occurring in a fixed interval of time or space, where these events occur with a known constant mean rate and independently of the time since the last event.

Discrete Random Variable

A random variable that can take on a countable number of distinct values, often representing quantities that can be enumerated.