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Cogito

Algebra 2 · Chapter 4 · Lesson 1

Practice Worksheet

Rational Functions and Extraneous Solutions

Where the graph breaks, and where answers go wrong.

10 problems · about 21 minutes · A-APR.D.6, A-REI.A.2, F-IF.C.7

NameDate

Figure — use these to answer the problems

The two branches never join. The gap is the asymptote.
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y = 1/x + 0
Numerator1
Shift up by0
Figure 1

Warm-Up Review

From earlier lessons. Loosen up before the new work.

2 problems

  1. From “Solving Polynomial Equations”

    x³ − 4x = 0. How many real roots?

    Answer

  2. From “Dividing Polynomials”

    f(x) = x² + 2, divided by (x − 3). Remainder?

    Answer

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. y = 1/(x − 7). At what x is it undefined?

    Answer

  2. Why can a rational equation produce an answer that does not work?

    • Multiplying by an expression that could be zero adds solutions.
    • You made an arithmetic error.

  3. y = 1/(x + 3). At what x is it undefined?

    Answer

  4. Solve 10/x = 5.

    Answer

Build It Up

The same ideas with more to keep track of.

2 problems

  1. Solve 12/x = 4.

    Answer

  2. Must you check answers to a rational equation?

    • Yes. Some are extraneous.
    • No.

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

2 problems

  1. The Asymptote

    y = 1/(x − 5). At what x is it undefined?

    Answer

  2. The Solve

    Solve 6/x = 3.

    Answer