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.

A2.16

Identify the effect on the graph of replacing f(x) by f(x) + k, k ∙ f(x), f(k ∙ x), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Extend to polynomial, trigonometric (sine and cosine), logarithmic, reciprocal, radical, and general piecewise functions.

Example Problems

Factor the expression as the product of two binomials.

5xp - 15xw - mp + 3mw

Factor the expression as the product of two binomials.

8xp - 12xw - 2mp + 3mw

Factor the expression as the product of two binomials.

12xp - 30xw + 2mp - 5mw

Khan Academy Resources

Function symmetry introduction Symmetry of polynomials Radical functions & their graphs Graph sinusoidal functions Even and odd functions: Graphs and tables Identify function transformations Graphs of logarithmic functions Scale functions horizontally Amplitude of sinusoidal functions from equation Graph sinusoidal functions: phase shift Scale & reflect absolute value graphs Construct sinusoidal functions Period of sinusoidal functions from equation Graphs of square and cube root functions Reflect functions Graphs of exponential functions Shift functions Scale functions vertically Scale & reflect parabolas Even & odd functions: Equations Shift absolute value graphs Modeling with sinusoidal functions: phase shift Midline of sinusoidal functions from equation Shift parabolas Modeling with sinusoidal functions Amplitude & period of sinusoidal functions from equation Transforming sinusoidal graphs: vertical & horizontal stretches Transforming sinusoidal graphs: vertical stretch & horizontal reflection Function symmetry introduction Trig word problem: modeling annual temperature Trig word problem: length of day (phase shift)Transforming exponential graphs Even and odd functions: Graphs Shifting absolute value graphs Scaling functions introduction Scaling & reflecting absolute value functions: graph Scaling & reflecting parabolas Even and odd functions: Tables Graphing logarithmic functions (example 1)Scaling functions horizontally: examples Shifting functions introduction Intro to parabola transformations Reflecting functions: examples Transforming exponential graphs (example 2)Shifting parabolas Shifting functions examples Scaling & reflecting absolute value functions: equation Graphing exponential functions Reflecting functions introduction Identifying function transformations Scaling functions vertically: examples Graphing shifted functions Even and odd functions: Equations Even and odd functions: Find the mistake Trig word problem: modeling daily temperature Sinusoidal function from graph Identifying horizontal squash from graph Graphing logarithmic functions (example 2)

1-on-1 AI tutoring aligned to A2.16. 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 →