The CAHSEE exam (or the California High School Exit Exam) was designed to be used by the state of California in order to assess if the students graduating from California high schools are able to demonstrate skills which support their (the students') grade-level competency. The test focuses upon skills in math, reading, and writing. This test is a requirement of all students who wish to receive a diploma in California.
That being said, not all states give students true exit exams. Some states simply test their students to see where they (the students and the school) are ranked in regards to the rest of the nation.
Texas is a state which does require students to take a test in order to graduate. Students in Texas take the TAKS (Texas Assessment of Knowledge and Skills) exam.
While I could not find specific information on transfer students, I would assume (based upon the sites information) that if you have not yet graduated, you will be required to take the TAKS.