Lesson 1

Inputs and Outputs

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Problem 1

Given the rule:

Function rule diagram, no input given, right arrow, rule is, divide by 4, then add 2, right arrow, no output given.

Complete the table for the function rule for the following input values: 

input 0 2 4 6 8 10
output

Solution

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Problem 2

Here is an input-output rule:

Function rule diagram, no input given, right arrow, rule is, write 1 if the input is odd; write 0 if the input is even, right arrow, no output given.

Complete the table for the input-output rule: 

input -3 -2 -1 0 1 2 3
output

Solution

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Problem 3

Andre’s school orders some new supplies for the chemistry lab. The online store shows a pack of 10 test tubes costs $4 less than a set of nested beakers. In order to fully equip the lab, the school orders 12 sets of beakers and 8 packs of test tubes.

  1. Write an equation that shows the cost of a pack of test tubes, \(t\), in terms of the cost of a set of beakers, \(b\).
  2. The school office receives a bill for the supplies in the amount of $348. Write an equation with \(t\) and \(b\) that describes this situation.
  3. Since \(t\) is in terms of \(b\) from the first equation, this expression can be substituted into the second equation where \(t\) appears. Write an equation that shows this substitution.
  4. Solve the equation for \(b\).
  5. How much did the school pay for a set of beakers? For a pack of test tubes?

Solution

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(From Unit 4, Lesson 15.)

Problem 4

Solve: \(\begin{cases} y=x-4 \\ y=6x-10\\ \end{cases}\)

Solution

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(From Unit 4, Lesson 14.)

Problem 5

For what value of \(x\) do the expressions \(2x+3\) and \(3x-6\) have the same value?

Solution

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(From Unit 4, Lesson 9.)