State the domain and the range of each relation. Then determine whether the relation is a function.
2 answers:
Answer:
{
}
{
}
The relation is not a function.
Step-by-step explanation:
By definition, a relation is a function if each input value has only one output value.
Given the relation:
(4,23)
(3,-2)
(-6,5)
(4,6)
The domain is the set of the x-coordinates of each ordered pair (You do not need to write 4 twice):
{
}
The range is the set of the y-coordinates of each ordered pair :
{
}
Since the input value 4 has two different output values (23 and 6), the relation is not a function.
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Answer:
Option A) The function is even because it is symmetric with respect to the y-axis.
Step-by-step explanation:
We are given a graph of the function.
We can see that the given function is symmetric around the y axis as the y axis acts as a mirror.
Symmetry around y-axis
- The y-axis acts as the line of symmetry for the given graph.
- A graph is said to be symmetric about the y axis if (a,b) is on the graph, then we can find the point (-a,b) on the graph as well.
Even Function:
- A function is said to be even if
- A function f is even if the graph of f is symmetric with respect to the y-axis
Odd function:
- A function is said to be odd if
- A function f is even if the graph of f is symmetric with respect to the x-axis.
Thus, we can write that the given function is an even function as the the graph is symmetric to the y-axis.
Option A) The function is even because it is symmetric with respect to the y-axis.
Answer:
1. a. b = - 8
b. x = 8
c. x = 11
d. x = 5
2. 12 soccer balls and 8 basketballs can be purchased.
Step by step explanation
a.
Calculate the sum
Collect like terms
Move variable to L.H.S and change it's sign
Similarly, Move constant to R.H.S and change its sign
Collect like terms
Change the signs on both sides of the equation
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b.
Apply cross product property
Multiply the numbers
Move constant to R.H.S and change its sign
Calculate the difference
Divide both sides of the equation by 5
Calculate
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c.
Apply cross product property
Multiply the numbers
Swap the sides of the equation
Move constant to R.H.S and change its sign
Calculate
Change the signs on both sides of the equation
Divide both sides of the equation by 8
Calculate
------------------------------------------------------------------
D.
Distribute 5 through the parentheses
Collect like terms
Swap both sides of the equation
Move constant to R.H.S and change its sign
Calculate the sum
Divide both sides of the equation by 11
Calculate
------------------------------------------------------------------
2.
Solution,
No.of students in soccer = x
No.of students in basketball = y
Total no.of students = 20
i.e x + y = 20 → equation ( i )
Cost of soccer ball = $ 7
Cost of basketball = $ 10
Total budget = $ 164
i.e 7x + 10 y = 165 → equation ( ii )
In equation ( i ),
x + y = 20
Move 'y' to R.H.S and change its sign
x = 20 - y
Put the value of x in equation ( i )
Now, put the value of y in equation ( i ) ,
x + y = 20
Hence, 12 soccer balls and 8 basketballs can be purchased.
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