Which is the graph of y = [x] - 2?
2 answers:
<h3>Answer: Top row, third option (far right)</h3>
Explanation:
The notation means "floor of x". Whatever decimal value x is, we just ignore the decimal portion and just focus on the integer part. We round down to the nearest whole number. We always round down.
For something like x = 2.5 or x = 2.7, the value of will be 2. It doesn't matter that 2.7 is closer to 3 than it is to 2. The interval
will be entirely on the x axis since we are taking the result of the flooring operation and subtracting off 2. Notice how x = 3 is not included. This is because x = 3 leads to y = 1 instead of y = 0. So we have an open hole at the end of the interval. The same goes for any other piece as well.
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<h3>Answer: Choice D</h3>
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Explanation:
The given equation is in slope intercept form y = mx+b
We see that m = 1/2 is the slope of y = (1/2)x-7
We'll use this slope along with the point (x1,y1) = (-3,-2) to get the following
Which is why choice D is the answer.
Note: this final equation is in point slope form.
<h2>Steps:</h2>
So for this, we will be completing the square to solve for m. Firstly, subtract 8 on both sides:
Next, divide both sides by 2:
Next, we want to make the left side of the equation a perfect square. To find the constant of this perfect square, divide the m coefficient by 2, then square the quotient. In this case:
-8 ÷ 2 = -4, (-4)² = 16
Add 16 to both sides of the equation:
Next, factor the left side:
Next, square root both sides of the equation:
Next, add 4 to both sides of the equation:
Now, while this is your answer, you can further simplify the radical using the product rule of radicals:
- Product rule of radicals: √ab = √a × √b
√12 = √4 × √3 = 2√3.
In exact form, your answer is
In approximate form, your answers are (rounded to the hundreths)