Two major components of your property tax calculation are Exemptions and Tax Rates which are both determined by your Taxing Units (School District, County, City, etc.). These are NOT determined by the Appraisal District or Tax Office.
Good News
The Texas Legislature allows you, the taxpayer, to attend the public hearings and meetings in which the Tax Rates are proposed and adopted by each Taxing Unit. You DO have a voice!
Note
The 86th Texas Legislature modified the manner in which the voter-approval tax rate is calculated to limit the rate of growth of property taxes in the state.