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Cogito

Grade 8 Math · Chapter 6 · Lesson 1

Practice Worksheet

What a Function Is

One output for every input.

10 problems · about 18 minutes · 8.F.A.1

NameDate

Figure — use these to answer the problems

A line gives exactly one height above each position. That is what makes it a function.
-10-10-5-5551010
y = 2x + 1
Slope2
Intercept1
Figure 1

Warm-Up Review

From earlier lessons. Loosen up before the new work.

2 problems

  1. From “Solving a System by Elimination”

    x + y = 12 and x − y = 4. What is x?

    Answer

  2. From “Solving a System by Substitution”

    y = 4x and x + y = 15. What is x?

    Answer

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. Rule "multiply by 4 then add 1". What comes out when 5 goes in?

    Answer

  2. What makes a rule a function?

    • Every input has exactly one output.
    • It is written as a formula.

  3. Rule "multiply by 3". What comes out when 6 goes in?

    Answer

  4. Is "double it" a function?

    • Yes.
    • No.

Build It Up

The same ideas with more to keep track of.

2 problems

  1. Rule "subtract 4". What comes out when 10 goes in?

    Answer

  2. Can one input give two outputs in a function?

    • No.
    • Yes.

Stretch Yourself

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

2 problems

  1. The Rule

    The rule is "add 7". What comes out when 5 goes in?

    Answer

  2. The Test

    A rule sends 4 to both 2 and −2. Is it a function?

    • No. One input gave two outputs.
    • Yes.