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In 2014, the unemployment rate of one county in California was 7%. In another county, the unemployment rate was 11%. Which of the following express...
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SAT Math 3.1 Algebra and Functions 250 Views
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SAT Math 3.1 Algebra and Functions
SAT Math 3.1 Algebra and Functions
Transcript
- 00:03
Here’s your shmoop du jour, brought to you by Real Numbers.
- 00:06
Seriously – they haven’t had any plastic surgery whatsoever.
- 00:10
G of x equals the square root of 4 minus x squared.
- 00:14
For which values of x is the equation true?
- 00:17
And here are the potential answers…
Full Transcript
- 00:20
Ok, so the question tells us we’re trying to find the values of x that make this square root function true.
- 00:27
Well, we know that since g of x involves a radical,
- 00:30
the only way this equation is true is if the stuff under the radical is non-negative.
- 00:37
Which…is just a fancy-shmancy way of saying zero or higher.
- 00:41
For this to happen, x squared can't be greater than 4.
- 00:44
In other words, x squared must be less than or equal to 4.
- 00:49
We can automatically eliminate answer choice E as “all real numbers”
- 00:52
To put this equation another way, x must be equal to or fall between -2 and 2.
- 00:59
Let’s try a number just to see if this works…
- 01:02
we’ll go with the ever popular zero. 4 minus 0 squared, or 4 minus 0, is 4.
- 01:08
And we can take the square root of 4… which equals plus or minus 2...
- 01:13
so looks like the equation is true for all numbers equal to or between negative 2 and 2.
- 01:20
And the answer’s C.
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