Provide an Appropriate Response $\mathrm { f } ( \mathrm { x } )$

question 74

Multiple Choice

Provide an appropriate response.
-If $\mathrm { f } ( \mathrm { x } )$ is one-to-one, can anything be said about $h ( x ) = 6 f ( x ) + 3$ ? Is it also one-to-one? Give reasons for your answer.

• A) Yes, \(h ( x )\) will be one-to-one. For every distinct value of \(f ( x )\) there is one distinct value of \(h ( x )\).
• B) No, \(h ( x )\) will not be one-to-one. The function \(h ( x )\) assumes the same value for at least two different \(f ( x )\)-values.
• C) Yes, \(h ( x )\) will be one-to-one. The inverse of \(f ( x )\) is \(h ( x )\) and is therefore one-to-one.
• D) No, \(h ( x )\) will not be one-to-one. The function \(h ( x )\) does not pass the horizontal line test.

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Definitions:

Nucleus Pulposus

The gel-like inner core of an intervertebral disc, which helps absorb shock and maintain flexibility of the spine.

Intervertebral Disks

The cartilaginous pads located between the vertebrae in the spine, acting as shock absorbers.

Vertebral Foramen

The central canal in a vertebra through which the spinal cord passes, protected by the vertebral arch.

Tibia

The larger, stronger, and anterior of the two bones in the lower leg, commonly referred to as the shin bone.