In a pool at a water park, a dolphin jumps out of the water traveling at 24 feet per second. its height h, in feet, above the wa
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The equation is undefined for singularity points at 0, 3, then c ≠ 0, c ≠ 3
<h3>What is the graph of the parent function (y)?</h3>The set of all coordinates (x, y) in the plane that satisfy the equation y = f(x) is the graph of the function. Suppose a function is only specified for a small set of input values, the graph of the function will only have a small number of points, in which each point's x-coordinate represents an input number and its y-coordinate represents an output number.
From the given information,
- The domain for the
is at x ≥ 0,
- The range is the set of values that the dependent variable for which the function is defined. f(x) ≥ 0.
In the second question:
Multiply by LCM
- c - (c - 3) = 3
Solve c - (c - 3) = 3: True for all c
c ≠ 0, c ≠ 3
Therefore, we can conclude that since the equation is undefined for singularity points at 0, 3, then c ≠ 0, c ≠ 3
Learn more about the graph of a function here:
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<span>Ayesha's right. There's a good trick for knowing if a number is a multiple of nine called "casting out nines." We just add up the digits, then add up the digits of the sum, and so on. If the result is nine the original number is a multiple of nine. We can stop early if we recognize if a number along the way is or isn't a multiple of nine. The same trick works with multiples of three; we have one if we end with 3, 6 or 9.
So </span>
<span>has a sum of digits 31 whose sum of digits is 4, so this isn't a multiple of nine. It will give a remainder of 4 when divided by 9; let's check.
</span>
<span>
</span>Let's focus on remainders when we divide by nine. The digit summing works because 1 and 10 have the same remainder when divided by nine, namely 1. So we see multiplying by 10 doesn't change the remainder. So
has the same remainder as 
.
When Ayesha reverses the digits she doesn't change the sum of the digits, so she doesn't change the remainder. Since the two numbers have the same remainder, when we subtract them we'll get a number whose remainder is the difference, namely zero. That's why her method works.
<span>
It doesn't matter if the digits are larger or smaller or how many there are. We might want the first number bigger than the second so we get a positive difference, but even that doesn't matter; a negative difference will still be a multiple of nine. Let's pick a random number, reverse its digits, subtract, and check it's a multiple of nine:
</span>
So </span>
</span>
</span>Let's focus on remainders when we divide by nine. The digit summing works because 1 and 10 have the same remainder when divided by nine, namely 1. So we see multiplying by 10 doesn't change the remainder. So
When Ayesha reverses the digits she doesn't change the sum of the digits, so she doesn't change the remainder. Since the two numbers have the same remainder, when we subtract them we'll get a number whose remainder is the difference, namely zero. That's why her method works.
<span>
It doesn't matter if the digits are larger or smaller or how many there are. We might want the first number bigger than the second so we get a positive difference, but even that doesn't matter; a negative difference will still be a multiple of nine. Let's pick a random number, reverse its digits, subtract, and check it's a multiple of nine:
</span>