Is Goblins free for teachers?

Yes. Goblins offers a generous free tier that includes 1 live feedback assignment per week, insights on student mastery and replays, and the ability to upload your own content. The Max plan adds unlimited assignments, superadaptive mode, grade exports, standards growth reports, and SSO/LMS integration, with per-student pricing for schools and districts.

How does Goblins work?

Three simple steps: (1) Share an assignment from thousands of standards-aligned topics using a share code. (2) Students speak and draw their thinking naturally, and Goblins responds with Socratic questioning that sounds just like their teacher. (3) Teachers get real-time formative insights showing what students struggle with and suggestions to inform instruction.

Does Goblins prevent cheating?

Yes. Goblins uses a purpose-trained AI model that evaluates cheating signals in real time. It can detect when students are copying answers, using external tools inappropriately, or not genuinely working through problems. Copy-pasting answers is also blocked.

Can I use my own voice with Goblins?

Yes. Teachers can record their voice and take a selfie to create a custom 3D avatar in about 30 seconds. Students then hear help in their own teacher's voice and see a familiar face, making the experience more personal and effective.

What math levels does Goblins cover?

Goblins covers math from Grade 5 through AP Calculus, including thousands of standards-aligned topics. Teachers can also upload their own content for custom assignments at any level.

Is Goblins FERPA compliant?

Yes. Goblins is FERPA and state compliant. Student data privacy and security are a top priority.

Does Goblins support English Language Learners?

Yes. Goblins supports 30+ languages so teachers don't have to translate every worksheet. It is especially helpful for ELL students who need accessible math instruction in their native language.

What grade level is PC.RFR.BF.2 taught?

This standard is part of the PC curriculum in Arizona Mathematics Standards.

Are there practice problems for PC.RFR.BF.2?

Yes, there are 3 practice problems available for PC.RFR.BF.2 with worked examples.

What learning resources are available for PC.RFR.BF.2?

There are 27 Khan Academy resources available for PC.RFR.BF.2, including 17 videos, 8 exercises, 2 articles.

PC.RFR.BF.2: Model relationships through composition and attend to the restrictions of the domain. | Arizona Mathematics Standards

Model relationships through composition and attend to the restrictions of the domain.

Example Problems

Find

\frac{d}{dx}(\cos(e^{x}))

Find

\frac{d}{dx}(\arcsin(-3x))

Find

\frac{d}{dx}(e^{\tan(4x)})

Khan Academy Resources

Composing functions Intro to composing functions Domain and range from graph Find composite functions Identifying values in the domain Function domain word problems Evaluate composite functions Model with composite functions Determine the domain of functions Evaluate composite functions: graphs & tables Examples finding the domain of functions Evaluating composite functions Modeling with composite functions Worked example: domain and range from graph Evaluating composite functions: using tables Intro to composing functions Worked example: determining domain word problem (real numbers)Meaningfully composing functions Evaluating composite functions: using graphs Modeling with composite functions: skydiving Determining whether values are in domain of function Worked example: determining domain word problem (positive integers)What is the domain of a function?Finding composite functions Worked example: determining domain word problem (all integers)Function notation word problem: bank Evaluating composite functions (advanced)

1-on-1 AI tutoring aligned to PC.RFR.BF.2. Instant help for students, real-time insights for teachers.

Used in classrooms by 100,000+ students at Baltimore County, Plano ISD, Deer Valley USD, KIPP, and districts nationwide.

Free for teachers, forever →