Cogito
Precalculus · Chapter 1 · Lesson 3
Symmetry, End Behaviour, and Continuity
Read a graph before you compute anything.
12 problems · about 22 minutes · TEKS P.2.A, TEKS P.2.I
Figure — use these to answer the problems
Warm Up
Straightforward practice. Get the method working first.
5 problemsf(x) = x⁴ − x². Even, odd or neither? 1, 2 or 3.
AnswerWhat decides the end behaviour of a polynomial?
- The leading term: its degree and its sign.
- The constant term.
f(x) = x². Even, odd or neither? 1, 2 or 3.
Answerf(x) = x³. Even, odd or neither? 1, 2 or 3.
Answerf(x) = x² + x. Even, odd or neither? 1, 2 or 3.
Answer
Build It Up
The same ideas with more to keep track of.
3 problemsf(x) = 3x⁵. How many ends go up?
Answerf(x) = x⁶. How many ends go up?
Answerf(x) = 1 ÷ (x − 3). At which x is it discontinuous?
Answer
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsSort each function by its symmetry.
Write each item under the heading it belongs to: x⁴ − 3 · x⁵ + x · cos x · sin x
Even
Odd
f(x) = −x³. As x runs far right, rise or fall? 1 for rise, 2 for fall.
AnswerThe Test
f(x) = x⁴ + 2. Is it even, odd or neither? Enter 1 for even, 2 for odd, 3 for neither.
AnswerThe Ends
f(x) = −2x⁴. As x runs far right, does the graph rise or fall? Enter 1 for rise, 2 for fall.
Answer