{"@context":"https://schema.org/","@type":"Quiz","name":"

The function $\\bm{f}$ is defined by $\\bm{f}(\\bm{x})=(-8)(2)^{x}+22$. What is the $y$-intercept of the graph of $\\bm{y}=\\bm{f}(\\bm{x})$ in the xy-plane?

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The function $\\bm{f}$ is defined by $\\bm{f}(\\bm{x})=(-8)(2)^{x}+22$. What is the $y$-intercept of the graph of $\\bm{y}=\\bm{f}(\\bm{x})$ in the xy-plane?

","comment":{"@type":"Comment","text":"

Choice A is correct. The $y$-intercept of the graph of $y=\\bm{f}(\\bm{x})$ in the $xy$-plane occurs at the point on the graph where $\\bm{x}=0$. In other words, when $\\bm{x}=0$, the corresponding value of $\\bm{f}(\\bm{x})$ is the $y$-coordinate of the $y$-intercept. Substituting $0$ for $\\bm{x}$ in the given equation yields $f(0)=(-8)(2)^{0}+22$, which is equivalent to $\\bm{f}(0)=(-8)(1)+22$, or $f(0)=14$. Thus, when $\\bm{x}=0$, the corresponding value of $\\bm{f}(\\bm{x})$ is $14$. Therefore, the $y$-intercept of the graph of $y=\\bm{f}(\\bm{x})$ in the $xy$-plane is $(0,14)$.

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

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

Choice D is incorrect. This could be the $y$-intercept for $\\bm{f}(\\bm{x})=(-8)(2)^{x}$, not $f(\\bm{x})=(-8)(2)^{x}+22$.

"},"encodingFormat":"text/markdown","text":"

The function $\\bm{f}$ is defined by $\\bm{f}(\\bm{x})=(-8)(2)^{x}+22$. What is the $y$-intercept of the graph of $\\bm{y}=\\bm{f}(\\bm{x})$ in the xy-plane?

","suggestedAnswer":[{"@type":"Answer","position":1,"encodingFormat":"text/html","text":"

$(0,2)$

"},{"@type":"Answer","position":2,"encodingFormat":"text/html","text":"

$(0,22)$

"},{"@type":"Answer","position":3,"encodingFormat":"text/html","text":"

$(0,-8)$

"}],"acceptedAnswer":{"@type":"Answer","position":0,"encodingFormat":"text/html","text":"

$(0,14)$

","comment":{"@type":"Comment","text":"

"},"answerExplanation":{"@type":"Comment","text":"

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-advanced-math-multiple-choice-question-6"}

The function $\bm{f}$ is defined by $\bm{f}(\bm{x})=(-8)(2)^{x}+22$. What is the $y$-intercept of the graph of $\bm{y}=\bm{f}(\bm{x})$ in the xy-plane?