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API Gateway supports AppSync but you can’t do with AppSync out-of-the-box yet is custom domain names. You can set up an HTTP proxy that routes traffic to the AppSync API, and then configure a custom domain name in API Gateway. This approach takes more work to set up and incurs higher cost and latency (compared to using CloudFront) because every request has to go through API Gateway so you can't easily declare an API Gateway without any Lambda functions.