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Two-Step Function Machines

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Two-Step Function Machines

Work through each rule in the order shown. For reverse problems, undo the operations in reverse order.

Follow the Rules

1.A machine multiplies its input by 4, then adds 3. What output does it give for an input of 6?

2.A machine subtracts 2 from its input, then multiplies the result by 5. Find the output for an input of 9.

3.Which expression represents the rule “multiply the input x by 3, then subtract 8”?

3(x - 8)
3x - 8
8x - 3
x - 24

4.Evaluate 5x + 2 when x = 4.

5.Match each two-step rule to its expression. Let x stand for the input.

Add 6, then multiply by 2
Multiply by 2, then add 6
Subtract 3, then multiply by 4
Multiply by 4, then subtract 3

4(x - 3)
2(x + 6)
4x - 3
2x + 6

Work Out the Missing Step

6.A machine starts with 7, multiplies by 2, and then uses a missing addition or subtraction to produce 10. What operation and number are missing?

7.An input of 5 goes through an unknown first operation, then has 4 added. The output is 19. The first operation is multiplication by a whole number. What is the first operation?

8.A machine multiplies an input by 5 and then adds 2. If its output is 32, what was the input?

9.Write an expression for a machine that subtracts 7 from input x and then multiplies the result by 3.

10.Write an expression for a machine that multiplies input x by 6 and then subtracts 5.

11.A machine follows the rule 4x + 1. What output does it give when x = 8?

Think About the Order

12.Use input 4 to compare these rules: (a) add 3, then multiply by 2; (b) multiply by 2, then add 3. Find both outputs.

13.Explain why changing the order of two operations can change an output. Use input 3 with the rules “add 4, then multiply by 2” and “multiply by 2, then add 4”.