Answer: 
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Explanation:
We start with y = 1/x
Vertically stretching it by a factor of 4 gets us to y = 4/x. Simply multiply the right hand side by 4.
Then reflecting over the y axis means we replace every x with -x to get y = 4/(-x) but that simplifies to y = -4/x. So we can see that any y axis reflection is identical to an x axis reflection, and vice versa. This is due to the symmetry of hyperbolas like this.
Next, we replace x with (x+5) so that we shift the xy axis 5 units to the right, giving the illusion the curve shifts 5 units to the left.
Lastly, we tack on a +4 to shift the graph up 4 units.
The final result is
<h3>Answer: 13</h3>
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Explanation:
The best case scenario is that you get 3 of the same color in a row on the first three attempts. The lower bound is 3.
However, we have to consider the worst case scenario when we want to guarantee something like this, without looking at the candies we selected.
Consider the case of something like this sequence:
- black
- white
- green
- red
- blue
- yellow
- black
- white
- green
- red
- blue
- yellow
- black
As you can see above, I've listed the colors in the order presented by your teacher. I pick one candy at a time. Once I reach yellow, I restart the cycle. In slots 1, 7 and 13, we have a black candy selected. This example shows that we must make 13 selections to guarantee that we get at least 3 candies of the same color (that color being black). The order of the candies selected doesn't matter. We could easily use any other color except yellow to do this example. The black candy just happened to be the first listed, so I went with that.
Note how we have 6 unique colors in the set {black, white, green, red, blue, yellow}. If we pick 2 candies of each color, then we've selected 6*2 = 12 candies so far. That 13th candy (some color other than yellow) is guaranteed to be a color we already selected; therefore, we'll be guaranteed to have 3 of the same color. We won't know what color it is but we will know we have a match like this.
For more information, check out the Pigeonhole Principle.
The answer should be A.
When we see the equation y=a^x we can relate to all the exponential functions, however, when the problem asked what points does all equations in that form pass through. I was instantly reminded by two facts.
One is that any number to the first is equal to itself. In other words, a^1=a
Another is that any number to the zero is equal to 1. a^x=1
if that is true, 1 will always be the x value since y=a^x and 0 will always be the x value because that is how y can be equal to one.
therefore, the answer is A: (0,1)
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