$3.$ Imagine Sarah, a graphic designer who has been running a small side business from her home for the past four years. She creates custom illustrations and sells them online through her website and social media platforms. However, Sarah's business has consistently generated minimal profit, with expenses exceeding her income each year. For the past four consecutive years, she has claimed net business losses and used them to offset her salary income from her primary job.

a$)$ What specific factors do the IRS and Tax Court consider when determining whether an activity like Sarah's graphic design business is conducted with a profit motive, and how do these factors influence the classification of the activity as a business or a hobby? Additionally, is Sarah$$s side business likely to be recharacterized as a hobby by the IRS in a given year and why? $($Include citations from relevant tax authorities in your answers.$)$

b$)$ How does the reclassification of a business as a hobby by the IRS affect the taxpayer's ability to claim losses, and what are the potential financial consequences for taxpayers like Sarah who rely on business losses to offset other income $($including citations from relevant tax authorities$)?$