Lesson 1
Inputs and Outputs
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.](https://cms-im.s3.amazonaws.com/hjNiM1S4fpmYJGmVjiTg7bVN?response-content-disposition=inline%3B%20filename%3D%228-8.5.New.Image.PP.82.png%22%3B%20filename%2A%3DUTF-8%27%278-8.5.New.Image.PP.82.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T171254Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=c8863806da2ddf67312e2dfa161c46165a04715f8dcecea338807dc286eb67b2)
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.](https://cms-im.s3.amazonaws.com/qz8MJpRTFn7ZDc8o6YUgv3xJ?response-content-disposition=inline%3B%20filename%3D%228-8.5.New.Image.PP.79.png%22%3B%20filename%2A%3DUTF-8%27%278-8.5.New.Image.PP.79.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T171254Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=c0640fb893841db8f5b73fb0b2bfcb55d22fd66974c5322549eca40b74b28248)
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.
- Write an equation that shows the cost of a pack of test tubes, \(t\), in terms of the cost of a set of beakers, \(b\).
- 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.
- 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.
- Solve the equation for \(b\).
- 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.)