Fiona, Fences, Wonderland and Sequences
Test Review
Vocabulary
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Function – set of ordered pairs in which all x values are paired with exactly one y-value
Linear function – function that graphs as a line
Vertical line test – way of testing a graph to see if it is a function
Function notation – efficient way to describe relationships between quantities that vary in a functional relationship
Domain – x-values, inputs, independent variables
Range – y-values, outputs, dependent variables
Independent variable – variables that are chosen, inputs
Dependent variable – variables that change because of the independent variables, outputs
Perimeter – distance around a figure
Area – size inside a figure
Maximum point – largest value of the output
Minimum point – smallest value of the output
Conditional Statement – statement in “if…then” format
Hypothesis – “if” portion of a conditional statement
Conclusion – “then” portion of a conditional statement
Converse – exchanging the hypothesis and conclusion
Negation – negating the hypothesis only
Inverse – negating the hypothesis and conclusion
Contrapositive – negating and exchanging the hypothesis and conclusion
Biconditional – “if and only if” form of a statement
Truth Value – whether a statement is true or false
Concepts
Evaluating Function Notation and Writing Equations in Function Notation
Given that 𝑓(𝑥) = 2𝑥 + 1, 𝑔(𝑥) = 𝑥 2 + 3𝑥 − 4 and ℎ(𝑥) = 5 − 𝑥 , find the following values.
1. 𝑓(−1)
Use the table to find the following values
5. 𝑓(0)
3. 𝑔(−2)
2. ℎ(𝑥) = −1, find x
x
f(x)
6. 𝑓(7)
9. Is the relation described in the table a function? Explain.
-3
12
-1
9
0
5
4. 𝑓(𝑥) = 9, find x
2
4
3
-2
7. if 𝑓(𝑥) = 2, then 𝑥 =
5
-1
7
-6
8. if𝑓(𝑥) = −3, then 𝑥 =
Given the following situations, write an equation in function notation. Tell what the independent and dependent variables
are in each situation.
10. Smith’s Cab Company charges a flat rate of $2.50 and $0.75 per mile to ride in the cab.
11. Kroger sells chicken for $1.99 per pound.
12. Joe makes 6 dollars an hour.
Anna’s mother and father said she could have a puppy on one condition: Anna had to build the puppy a rectangular pen
in the backyard before she could get the puppy. Anna’s dad has 20 fencing panels each 1 meter left over from doing the
entire yard. The panels cannot be cut, and Anna wants to use all the panels.
13. Make a table showing all the possible integer values for x (length) and y (width) of the pen.
x
y
14. Write an equation in function notation relating the y-dimension to the x-dimension.
15. Write an equation in function notation for the area of the pen.
16. Extend the table to show the possible areas of the pen.
17. Graph the relationship between the x-dimension and the area of the pen.
18. Should the dots be connected? Explain.
19. What dimensions should Anna build the pen in order to give the puppy the maximum area? What is the maximum
area?
20. Describe a situation in which the dots in the above graph should be connected.
Mathematical Arguments
21. Given the statement below, write each of the following.
If 𝒙 = −𝟐, then𝒇(𝒙) = 𝟔.
Hypothesis
Conclusion
Converse
Negation
Inverse
Contrapositive
Biconditional
Absolute Value Functions
Use a table of values to graph the following functions.
22. 𝑓(𝑥) = 2|𝑥 − 1|
-15
23. 𝑔(𝑥) = −|𝑥| + 3
x
x
y
y
-10
10
10
8
8
6
6
4
4
2
2
-5
5
-1510
-1015
-5
5
-2
-2
-4
-4
-6
-6
-8
-8
-10
-10
-12
-12
10
15