Answer:
In inequality notation:
Domain: -1 ≤ x ≤ 3
Range: -4 ≤ x ≤ 0
In set-builder notation:
Domain: {x | -1 ≤ x ≤ 3 }
Range: {y | -4 ≤ x ≤ 0 }
In interval notation:
Domain: [-1, 3]
Range: [-4, 0]
Step-by-step explanation:
The domain is all the x-values of a relation.
The range is all the y-values of a relation.
In this example, we have an equation of a circle.
To find the domain of a relation, think about all the x-values the relation can be. In this example, the x-values of the relation start at the -1 line and end at the 3 line. The same can be said for the range, for the y-values of the relation start at the -4 line and end at the 0 line.
But what should our notation be? There are three ways to notate domain and range.
Inequality notation is the first notation you learn when dealing with problems like these. You would use an inequality to describe the values of x and y.
In inequality notation:
Domain: -1 ≤ x ≤ 3
Range: -4 ≤ x ≤ 0
Set-builder notation is VERY similar to inequality notation except for the fact that it has brackets and the variable in question.
In set-builder notation:
Domain: {x | -1 ≤ x ≤ 3 }
Range: {y | -4 ≤ x ≤ 0 }
Interval notation is another way of identifying domain and range. It is the idea of using the number lines of the inequalities of the domain and range, just in algebriac form. Note that [ and ] represent ≤ and ≥, while ( and ) represent < and >.
In interval notation:
Domain: [-1, 3]
Range: [-4, 0]
Answer:
The y intercept is 1
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = 2x+b
Substitute the point into the equation and solve for y
3 = 2(1)+b
3 =2+b
1 = b
The y intercept is 1
Answer:
-23x = 7
Step-by-step explanation:
-3x - y =0
×5. ×5 ×5
-15x -5y = 0
-8x +5y = 7
-15x -5y -0
-23x = 7
Answer:
x=31/25
Step-by-step explanation:
3x+4/5=7-2x
Multiply through by 5
5(3x+4/5)=5(7-2x)
15x+4=35-10x
Collecting like terms
15x+10x=35-4
25x=31
x=31/25
220 degrees = 3.83972
to convert degrees to radians, multiply by <span>π<span>180°</span></span>, since a full circle is <span>360°</span> or <span>2π</span> radians.<span>220°⋅<span>π<span>180°</span></span></span> radians Cancel the common factor of 20 <span><span>111</span>⋅<span>π9</span></span> radians Multiply <span>111</span>and <span>π9</span> to get <span><span>11π</span>9<span>11π</span>9</span><span> radians
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</span><span>I hope this helps.</span>
