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

In the linear function $f$, $f(0)=8$ and $f(1)=12$. Which equation defines $f$?

","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-119"}],"about":{"@type":"Thing","name":"Math, Algebra, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Algebra","Duplicate"],"name":"

In the linear function $f$, $f(0)=8$ and $f(1)=12$. Which equation defines $f$?

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

Choice $D$ is correct. Since $f$ is a linear function, it can be defined by an equation of the form $f(x)=ax+b$, where $a$ and $b$ are constants. It's given that $f(0)=8$. Substituting $0$ for $x$ and $8$ for $f(x)$ in the equation $f(x)=ax+b$ yields $8=a(0)+b$, or $8=b$. Substituting $8$ for $b$ in the equation $f(x)=ax+b$ yields $f(x)=ax+8$. It's given that $f(1)=12$. Substituting $1$ for $x$ and $12$ for $f(x)$ in the equation $f(x)=ax+8$ yields $12=a(1)+8$, or $12=a+8$. Subtracting $8$ from both sides of this equation yields $a=4$. Substituting $4$ for $a$ in the equation $f(x)=ax+8$ yields $f(x)=4x+8$. Therefore, an equation that defines $f$ is $f(x)=4x+8$.

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.

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

In the linear function $f$, $f(0)=8$ and $f(1)=12$. Which equation defines $f$?

","suggestedAnswer":[{"@type":"Answer","position":0,"encodingFormat":"text/html","text":"

$f(x)=12x+8$

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

$f(x)=4x$

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

\$f(x)=4x+12\$

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

$f(x)=4x+8$

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

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

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-algebra-multiple-choice-question-119"}