Algebra Name
Algebra Name _______________________
1st Linear Quiz Review Sheet Block ______
Check for understanding:
1) How do I recognize that I have a linear equation?
2) What does the graph of a linear equation look like?
3) Why do we use arrows when graphing a linear equation?
4) Is a linear equation always a function?
5) How do I recognize that a relation is a function if I’m given a set of ordered pairs or an input-output table?
6) How do I recognize that a graph is a function (and not just a relation)?
7) Can a linear equation have only one variable?
8) Can a linear equation contain the product of 2 variables?
9) What is the domain of a relation?
10) What is the range of a relation?
11) How do you rewrite an equation into function form?
12) What does function notation look like? What represents the input and what represents the output?
13) How do I check if an ordered pair is a solution to a linear equation?
Determine which of the ordered pairs is a solution to the equation. Show all work.
14) [pic] ; [pic] ; [pic]
15) [pic] ; [pic] ; [pic]
Identify the Domain and Range and Explain why the relation is/is not a function:
|input |3 |1 |-1 |3 |
|output |1 |2 |3 |4 |
16)
17) [pic]
18)
19) Evaluate the function [pic] for [pic]
20) Find the values of [pic] such that the function [pic] has the values of:
a) [pic] b) [pic] c) [pic] d) [pic]
Find the intercepts, write as ordered pairs, and graph the lines:
21) [pic]
22) [pic]
23) [pic]
Write each equation in function form, find 3 solutions and graph:
24) [pic]
25) [pic]
26) [pic]
27) [pic]
28) [pic]
29) [pic]
30)
1st Linear Quiz Review Sheet – Answers
1) A linear equation has at most 2 variables, each to the 1st power and no products of variables.
2) The graph of a linear equation is always a line.
3) We use arrows on the ends of the line to represent the infinite # of solutions.
4) Linear equations are not always functions. Vertical lines are the only lines that are NOT functions.
5) The relation is a function if each input is used only once.
6) If a graph is a function, then a vertical line will only touch the function once. It must “pass” the vertical line test.
7) Yes, the equations of vertical and horizontal lines each contain only one variable.
8) No, a linear equation may NOT contain the product of 2 variables.
9) The domain is the set of all inputs.
10) The range is the set of all outputs.
11) To write an equation in function form, we apply the properties of equality to isolate y.
12) Function notation is, for example, [pic]. The input is [pic] and the output is [pic].
13) I check if an ordered pair is a solution by substituting the x and y values into the equation. If the statement is true, then the ordered pair IS a solution. If the statement is false, then the ordered pair is NOT a solution.
14) [pic] is a solution.
15) [pic] is a solution.
16) Domain: [pic] Range: [pic] Not a function because 3 is used twice as an input.
17) Domain: [pic] Range: [pic] This is a function because each input is only used once.
18) [pic] ; [pic] , [pic]
19) a) [pic] b) [pic] c) [pic] d) [pic]
20) [pic] and [pic]
21) [pic] and [pic]
22) [pic] and [pic]
23) [pic]
24) [pic]
25) can’t be!
26) [pic]
27) already is!
28) [pic]
29)
30)
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