Unit 10: Functions and Patterns
What makes an input-output rule a function, how to spot one on a graph, and the patterns that repeat with a fixed rule.
4 topics · 13 questions
Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.
What a Function Is
- How it worksHow does a function assign exactly one output to every input it's given?
- Common mistakeWhy doesn't a function need to be written as an equation to actually be a function?
- Going furtherWhat happens to whether a rule is a function if you swap which variable is the input and which is the output?
Your turn1 of 2
A vending machine's price list assigns exactly one price to each button. A different rule assigns TWO different output values to input 7, though every other input still gets just one. Which one is a function?Function Tables
- How it worksHow do you fill in a function table by applying the same rule to every input value?
- Worked exampleBuild a function table for the rule y equals 3x minus 2, using the inputs negative 1, 0, 1, and 2.
- Worked exampleFind the rule that produces the outputs 5, 8, 11, 14 from the inputs 1, 2, 3, 4.
Your turn1 of 2
A vending machine's rule for change given is y equals 7x minus 6, where x is the number of coins inserted. Find y, the change given, when x is 9.The Vertical Line Test
- How it worksHow does a vertical line crossing a graph more than once reveal an input with two different outputs?
- Worked exampleFind whether a circle graphed on the coordinate plane passes the vertical line test.
- Common mistakeWhy doesn't a graph that curves or loops automatically fail the vertical line test?
Your turn1 of 2
A vertical line drawn through a graphed circle crosses the circle at two points, for most positions of the line. Does the circle pass the vertical line test?Sequences and Patterns
- How it worksHow does finding the constant amount added each time let you write a rule for any term in the sequence?
- Worked exampleFind the 10th term of the sequence 3, 7, 11, 15.
- Common mistakeWhy doesn't a sequence like 2, 4, 8, 16 follow the same add-a-constant rule as 3, 7, 11, 15?
- Ties togetherHow does the constant amount added in an arithmetic sequence show up as the slope of its graph?
Your turn1 of 2
A stack of chairs starts with 14 chairs and gains 7 more each row. Find the number of chairs in the 28th row.