Interval notation is used to write a set of real numbers from one value to another value.
On the left, you start with left parenthesis or left bracket.
Then you follow by two numbers separated by a comma.
You then finish with a right parenthesis or right bracket.
To include a number, use a square bracket.
To exclude a number use parenthesis.
To write the set of numbers, you need to list the smallest number in the set followed by the largest number in the set. An interval is always stated with two numbers, from the smallest in the set to the largest in the set. The numbers are always separated by a comma.
Examples:
1) All numbers from 6 to 10, including 6 and 10.
Algebra: 6 <= x <= 10
Interval: [6, 10]
Notice brackets since both 6 and 10 are included in this interval.
2) All number from 5 to 20, including 5 but not including 20.
Algebra 5 <= x < 20
Interval: [5, 20)
Bracket with 5 means include 5. Parenthesis with 20 means 20 is not included.
3) All numbers greater than or equal to 7.
Algebra: x >= 7
Interval: [7, ∞)
The 7 has a bracket because it is included. Infinity always has parenthesis.
With the infinity symbol, always use parenthesis, not square bracket.
4) All numbers less than -5.
Algebra: x < - 5
Interval: (-∞, 5)
Now for your problems.
10.
This is a line. Both the domain and range all all real numbers.
That means the interval is from negative infinity to positive infinity.
(-∞, ∞)
Both the domain and range are that same interval, all real numbers, from negative infinity to positive infinity.
13.
The domain is all real numbers as you can see the x-coordinates extend left forever and right forever. The domain is the same interval as the domain and range of problem 10.
The range is zero and all positive numbers.
You can think of it a all values of y such that y is greater than or equal to zero. Notice that zero is included in the interval.
[0, ∞)
Since zero is included, we use a left bracket, not left parenthesis.
With infinity, we alyways use parentheses, not brackets.
Set the 2x - 1 equal to 9 then work backwards. 2x - 1 = 9 Nine minus one is eight divided by two is four. X = 4
Answer:
Option B
Step-by-step explanation:
we know that
A line perpendicular to the x-axis is a line parallel to the y-axis
so
the equation of the line is of the form x=(+/-)a
The slope of the line is undefined
where
a is a real number
therefore
x=6 is a line perpendicular to the x-axis
Answer:
1
Step-by-step explanation:
The following equations is equivalent to the slope formula is A) y₂= m(x₂-x₁) + y₁.
<h3>What is slope?</h3>
The angle of inclination of a line with respect to the horizontal is quantified. In analytical geometry, a line, ray, or line segment's slope is the proportion of the vertical to the horizontal distance between any two points ("slope equals rise over run").
<h3>What is equation?</h3>
Two expressions are combined by the equal sign to form a mathematical statement known as an equation. For instance, a formula might be 3x - 5 = 16. We discover that the variable x has a value of 7 after solving this equation.
Given that,
Take a look at the formula below for the slope between two coordinate locations, m.
m = 
Here, slope is
m = 
Where m is the slope and y₁ and y₂ and x₁ and x₂ are coordinates of the axis.
The first step is to multiply x₂-x₁ on both sides in order to acquire y₂ on its own.
so you must add y₁ to both sides in order to get y₂ alone.
m(x₂-x₁) +y₁ = y₂.
Therefore, the following equations is equivalent to the slope formula is A) y₂ = m(x₂-x₁) + y₁.
To know more about the slope, visit:
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