Multi-step equations using the distributive property
Types of Solutions
Mixed Equations
Function or Relation
Is it a function?
Mixed Functions
100
7(x-2)=6x
x= 14
100
Name the three different types of solutions for equations.
One solution, infinite solutions, no solution
100
2x+5= 3x
x = 5
100
Given the relation R = {(1,2), (3,4), (5,6)}, determine if this is a function.
Answer: Yes, this is a function.
Reasoning: There are no repeated x-values
100
Looking at the graph below, determine if this relation is a function. Explain why or why not.
No, this is not a function. Looking at the graph, there are two y-values (points) for x = -1.
100
The name of the test used to determine whether a graph is a function or not is called the ____________ _______ test.
Vertical Line
200
-(a-12)+4a= 9a
x= 2
200
If after solving the equation you arrive at 5 = -5, what is the type of solution?
no solution
200
7(d-1)=6d
d = 7
200
Looking at the table below, is this relation a function?
| x | y |
|---|---|
| 1 | 2 |
| 2 | 4 |
| 3 | 6 |
Yes, this is a function because:
- Each x-value appears exactly once
- Each x-value is paired with exactly one y-value
200
In the graph, we see a semi-circle. Is this relation a function? Explain using the vertical line test.
Yes, this is a function. When applying the vertical line test, any vertical line will intersect the semi-circle at most once.
200
State the range of the function {(4,-2),(-1,1),(2,-3),(3,0)}
{-3,-2,0,1}
300
3(x+1)=x+5
x= 1
300
If you arrive at the step 6=6 when solving an equation, what would be the solution?
infinite solutions
300
3(p+1)+2p=13
p=2
300
Given the relation R = {(1,2), (1,3), (2,4)}, determine if this is a function.
No, this is not a function.
Reasoning: The input of 1 has two outputs.
300
Looking at the graph, which shows a circle centered at the origin, explain why this is not a function and identify the x-values where it fails the vertical line test.
This is not a function. The vertical line test fails
300
Find the domain and range of {(-3,4),(0,10),(11,8),(4,5)}
Domain: {-3,0,4,11}
Range: {4,5,8,10}
400
4(2a+3)= -3(a-1)+31
x=2
400
If you arrive at 6x+2=6x+2 when solving the equation, what type of solution can you predict this is?
infinite solutions
400
-9 - b = 8b
b = -1
400
Is this relation a function?
| x | y |
|---|---|
| 1 | 3 |
| 1 | 4 |
| 2 | 5 |
No, this is not a function because:
- The x-value 1 is paired with two different y-values (3 and 4)
- A function must have exactly one output for each input
400
Write all the ordered pairs shown in the mapping diagram below. Then determine if it is a function or not.
{(10,15),(20,45),(30,25),(40,35)}
It is a function.
400
In an ordered pair, which number represents the domain and which number represents the range?
(x,y)
500
- (7 + 7v) = -10v + 8
x= 5
500
Fill in the blank so that the answer will be no solutions
5x - 4 = _____x + 2
5
500
10r+9(4r-17)=-15
r=3
500
The table shows test scores for different students. Is this a function if x represents students and y represents scores?
| Student (x) | Score (y) |
|-------------|-----------|
| Alice | 85 |
| Bob | 92 |
| Charlie | 85 |
| David | 78 |
Yes, this is a function because:
- Each student (input) appears exactly once
- Each student has exactly one score (output)
500
Look at the table below:
There's a question mark for one of the inputs. Which values could you put in that spot to make this NOT a function? (List all four values!)
32, 14, -2, and -10
500
Name three ways to represent a relation.
Ordered pairs, graph, mapping diagrams