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.

AIII.A.18

Find the composite of two given functions and find the inverse of a given function. Extend this concept to discuss the identity function f(x) = x.

Example Problems

What is the inverse of the function?

f(x) = 8x + 1

What is the inverse of the function?

f(x) = 7x + 1

What is the inverse of the function?

f(x) = 5x - 7

Khan Academy Resources

Intro to inverse functions Composing functions Intro to composing functions Verifying inverse functions by composition Intro to invertible functions Verify inverse functions Find composite functions Restrict domains of functions to make them invertible Evaluate inverse functions Evaluate composite functions Determine if a function is invertible Find inverses of rational functions Finding inverses of linear functions Model with composite functions Evaluate composite functions: graphs & tables Intro to inverse functions Finding inverse functions: linear Evaluating composite functions Modeling with composite functions Evaluating composite functions: using tables Intro to composing functions Graphing the inverse of a linear function Verifying inverse functions by composition Meaningfully composing functions Finding inverses of rational functions Evaluating composite functions: using graphs Restricting domains of functions to make them invertible Modeling with composite functions: skydiving Determining if a function is invertible Finding composite functions Inputs & outputs of inverse functions Verifying inverse functions from tables Verifying inverse functions by composition: not inverse Function notation word problem: bank Evaluating composite functions (advanced)

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