Algebra 1 Name
Parent Function Characteristics and Vocabulary (worksheet at the end)
Note: Students have already had some practice with graphing functions via a table of values and substitution. This activity will introduce the vocabulary associated with graphing.
Resources: index cards with one vocabulary word per card, pencils, paper, and graph paper.
Activity: Make a set of index cards that contain the terms below. More than one pair of cards may be needed, depending on class size. Each student should have a card. The students should get into two groups. Each group member should have an index card with a word that has the same meaning/value as the one on his/her card. Each group should provide a concise definition for their words. One person should give the group’s definition to the class. Next, each student should find his/her vocabulary partner. For example, if a student’s card reads, “input”, they will pair up with someone who has the “output” card. Once they find their vocabulary partner, they should work in those pairs for the remainder of the class period.
Word pairs:
Group A Group B
Input / Outputx / y
x / f(x)
Domain / Range
Independent variable / Dependent variable
a / f(a)
x-coordinate / y-coordinate
x-value / y-value
A brief discussion can follow to compare definitions. Address any issues with the definitions and notation.
Next, students will locate their parent graphs from a previous lesson. They should make sure their axes are correctly labeled and that each graph is labeled with its corresponding equation. Questions are on student worksheet.
Parent Functions:
1. Y = x
2. Y = x2 (why are all y values always nonnegative?)
3. F(x) = | x| (why are all f(x) values nonnegative?)
4. F(x) = x3
5. Y = 5 (bonus: describe the domain and range)
6. Y = √x
7. F(x) = 1/x
8. Input value = x; output value = 2x
Algebra 1: Function Characteristics and Vocabulary
Name
(Note: You will need your parent graphs and tables for this assignment.)
Using the function graphs for y = x2 and f(x) = | x|, provide a brief response for items #1-6.
1. Do these graphs open upward or downward? Why?
2. Now, write the ordered pair that represents lowest point on the graph. This is the graph's vertex. If you turn your graph upside down, what can you now say about the vertex? Using these two responses, write a brief definition for the word vertex.
3. What do you notice about the range values when the domain values are 1 and -1? Why does this happen?
4. For these two functions, draw a vertical line that goes through the vertex. What does this vertical line do to the graph?
This is the function's the axis of symmetry. Select three ordered pairs that are located on the on the axis of symmetry and write their coordinates here: What do you notice? If you had to write an equation for this line, what would it be?
5. Locate two ordered pairs in the table of values with the same input values. What do you notice about their corresponding output values?
6. Why is “x” the independent variable? Why is “y” the dependent variable? What does it “depend” on?
Now, using all eight parent function graphs, answer the following:
7. Which function graph(s) contain the origin?
8. Look at the graph(s) from left to right and write down the trends you see. (Which graph(s) increase from left to right? Which graph(s) decrease from left to right? Which graph(s) change directions? Which graph(s) is/are a straight line?) Write your observations next to the parent graphs you already have.
9. Which parent function(s) can have negative values in the range?
10. Which function(s) will never have an independent variable value of zero? Why not?
11. Look at each table of values for the parent functions. Which graphs contain an ordered pair on the x-axis? This is the function’s x-intercept. Which graphs contain an ordered pair on the y-axis? What do you think this is called?
12. A zero or a root is the name given to ordered pairs with a y-coordinate of zero. Next to each graph, locate the zero(s), if any, of each parent function.