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Advanced Math / Nonlinear functions Difficulty: Medium

The graph gives the estimated number of catalogs $y$ , in thousands, a company sent to its customers at the end of each year, where $x$ represents the number of years since the end of $1992$ , where $0 \leq x \leq 10$ . Which statement is the best interpretation of the y-intercept in this context?

The estimated total number of catalogs the company sent to its customers during the first $10$ years was $9,000$ .

The estimated total number of catalogs the company sent to its customers from the end of $1992$ to the end of $2002$ was $90$ .

The estimated number of catalogs the company sent to its customers at the end of $1992$ was $9$ .

The estimated number of catalogs the company sent to its customers at the end of $1992$ was $9,000$ .

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Explanation

Choice D is correct. The y-intercept of the graph is the point at which the graph crosses the y-axis, or the point for which the value of $x$ is $0$ . Therefore, the y-intercept of the given graph is the point $left parenthesis 0 comma 9 right parenthesis$ . It's given that $x$ represents the number of years since the end of $1992$ . Therefore, $x equals 0$ represents $0$ years since the end of $1992$ , which is the same as the end of $1992$ . It's also given that $y$ represents the estimated number of catalogs, in thousands, that the company sent to its customers at the end of the year. Therefore, $y equals 9$ represents $9,000$ catalogs. It follows that the y-intercept $left parenthesis 0 comma 9 right parenthesis$ means that the estimated number of catalogs the company sent to its customers at the end of $1992$ was $9,000$ .

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.