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.

MA.912.C.1.10

Given the graph of a function, identify whether a function is continuous at a point. If not, identify the type of discontinuity for the given function.

Example Problems

Which of the following functions are continuous for all real numbers?

g(x) = 2x + 5

h(x) = |x|

Which of the following functions are continuous for all real numbers?

g(x) = \ln(x^2 + 4)

h(x) = x^2

Which of the following functions are continuous for all real numbers?

g(x) = x^4 - 7x + 2

h(x) = 5^x

Khan Academy Resources

Continuity over an interval Continuity at a point (graphical)Classify discontinuities Worked example: Continuity at a point (graphical)Functions continuous at specific x-values Functions continuous on all real numbers Continuity at a point Types of discontinuities Continuity over an interval

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