Whole numbers<span><span>\greenD{\text{Whole numbers}}Whole numbers</span>start color greenD, W, h, o, l, e, space, n, u, m, b, e, r, s, end color greenD</span> are numbers that do not need to be represented with a fraction or decimal. Also, whole numbers cannot be negative. In other words, whole numbers are the counting numbers and zero.Examples of whole numbers:<span><span>4, 952, 0, 73<span>4,952,0,73</span></span>4, comma, 952, comma, 0, comma, 73</span>Integers<span><span>\blueD{\text{Integers}}Integers</span>start color blueD, I, n, t, e, g, e, r, s, end color blueD</span> are whole numbers and their opposites. Therefore, integers can be negative.Examples of integers:<span><span>12, 0, -9, -810<span>12,0,−9,−810</span></span>12, comma, 0, comma, minus, 9, comma, minus, 810</span>Rational numbers<span><span>\purpleD{\text{Rational numbers}}Rational numbers</span>start color purpleD, R, a, t, i, o, n, a, l, space, n, u, m, b, e, r, s, end color purpleD</span> are numbers that can be expressed as a fraction of two integers.Examples of rational numbers:<span><span>44, 0.\overline{12}, -\dfrac{18}5,\sqrt{36}<span>44,0.<span><span> <span>12</span></span> <span> </span></span>,−<span><span> 5</span> <span> <span>18</span></span><span> </span></span>,<span>√<span><span> <span>36</span></span> <span> </span></span></span></span></span>44, comma, 0, point, start overline, 12, end overline, comma, minus, start fraction, 18, divided by, 5, end fraction, comma, square root of, 36, end square root</span>Irrational numbers<span><span>\maroonD{\text{Irrational numbers}}Irrational numbers</span>start color maroonD, I, r, r, a, t, i, o, n, a, l, space, n, u, m, b, e, r, s, end color maroonD</span> are numbers that cannot be expressed as a fraction of two integers.Examples of irrational numbers:<span><span>-4\pi, \sqrt{3}<span>−4π,<span>√<span><span> 3</span> <span> </span></span></span></span></span>minus, 4, pi, comma, square root of, 3, end square root</span>How are the types of number related?The following diagram shows that all whole numbers are integers, and all integers are rational numbers. Numbers that are not rational are called irrational.
Step 1 = Distributive Property ( multiplying the 2 by each term in parenthesis)
Step 2 = Addition Property ( adding like terms)
Step 3 = Addition Property (adding 34x to each side)
Step 4 = Division Property. ( dividing both sides by 17)
If you describe the graph as a V with its vertex point on (0,0), then you are either describing the graph of y = |x| or y = 3|x|. The only difference is that the coordinates of y=3|x| is multiplied thrice the coordinates of y=|x|. In other words, this graph is thrice wider than the y=|x|.
Furthermore, <span>y = -3|x| is a downward V, and
</span>x = |y| and <span>x = 3|y| looks like a V rotated side-ward,</span><span>
</span>
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
Remember that the denominator cannot be equal to zero
so
The value of x cannot be equal to x=-2
<em>Simplify the numerator</em>
----> by difference of squares
substitute
simplify
The domain is all real numbers except the value of x=-2
The y-intercept is the point (0,-6) ---> value of y when the value of x is equal to zero)
The x-intercept is the point (2,0) ---> value of x when the value of y is equal to zero)
therefore
The graph in the attached figure
