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

The graph of $y=f(x)+14$ is shown. Which equation defines function $f$?

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","hasPart":{"@type":"Question","typicalAgeRange":"12-22","educationalAlignment":[{"@type":"AlignmentObject","alignmentType":"educationalSubject","targetName":"SAT"},{"@type":"AlignmentObject","alignmentType":"educationalLevel","targetName":"SAT","educationalFramework":"Common Core","targetUrl":"https://classnotes.xyz/mcqs/sat-math-algebra-multiple-choice-question-249"}],"about":{"@type":"Thing","name":"Math, Algebra, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Algebra","Duplicate"],"name":"

The graph of $y=f(x)+14$ is shown. Which equation defines function $f$?

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

Choice A is correct. An equation for the graph shown can be written in slope-intercept form $y=mx+b$, where $m$ is the slope of the graph and its $y$-intercept is $(0,b)$. Since the $y$-intercept of the graph shown is $(0,2)$, the value of $b$ is $2$. Since the graph also passes through the point $(4,1)$, the slope can be calculated as $\\dfrac{1-2}{4-6}$, or $-\\dfrac{1}{4}$. Therefore, the value of $m$ is $-\\dfrac{1}{4}$. Substituting $-\\dfrac{1}{4}$ for $m$ and $2$ for $b$ in the equation $y=mx+b$ yields $y=-\\dfrac{1}{4}x+2$. It's given that an equation for the graph shown is $y=f(x)+14$. Substituting $f(x)+14$ for $y$ in the equation $y=-\\dfrac{1}{4}x+2$ yields $f(x)+14=-\\dfrac{1}{4}x+2$. Subtracting $14$ from both sides of this equation yields $f(x)=-\\dfrac{1}{4}x-12$.

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 and may result from conceptual or calculation errors.

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

The graph of $y=f(x)+14$ is shown. Which equation defines function $f$?

$\"\"$

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

$f(x)=-\\dfrac{1}{4}\\,x+16$

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

$f(x)=-\\dfrac{1}{4}\\,x+2$

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

$f(x)=-\\dfrac{1}{4}\\,x-14$

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

$f(x)=-\\dfrac{1}{4}\\,x-12$

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

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

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-algebra-multiple-choice-question-249"}