# Precalculus – Domain of a function

Q: What is the domain of this function?

‘Like’ if you got it!

Explanation:

The domain of a function is a description of the x-values that may be plugged into the function. For a square root function, the restriction is that the number under the radical must not be negative. Therefore,

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# ACT, Geometry – diagonal of a rectangular prism

Q: What is the (straight-line) distance between points A and B on the figure below?

Explanation:  We are finding the length of the green segment below:

This requires the three-dimensional version of the distance formula:

There is another way to do this, using a progression of two right triangles, with the green segment being the hypotenuse of the second triangle, but I find the above formula much simpler.  It is just an extension of the ‘usual’ (2-dimensional) distance formula we are so familiar with from Algebra and Geometry.

BUT if you want an even easier way, and I know you do, use my TI-84 Plus program ‘DIST3D’.

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# Algebra 2 – exponential functions

Q: In 2010, River City had a population of 500. If the population has increased by 6% each year since then, what is the population this year, in 2014?

Explanation:

Alternatively,

Calcululate 6% of 500 by doing .06 * 500 = 30.

Increase 500 by 30, and you find that the population is 530 in 2011.

Now, increase 530 by 6% (530*.06, added to 530, or shortcut is to do 530*1.06).

The population is 561.8 in 2012. Don’t round this number yet – not until you get to the end of the problem.

Doing this calculation 2 more times gives you 595.508 for 2013 and 631.23… for 2014.

Now, round to the nearest whole number: 631. It’s not the most efficient way, but you get the right answer.

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# Precalculus – Probability

Q: In a group of 10 randomly chosen people, what is the probability that at least two people share the same birthday? (same month and day)

Explanation: (For simplicity, this explanation doesn’t take into account people with leap-day birthdays, but it wouldn’t change the answer by much!)

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# Precalculus – logarithms

Q: Solve the following equation involving logarithms:

Explanation:

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# Trig / Precalculus – convert degrees to radians

Q: Convert from degrees to radians:  330°

Explanation:

My TI-84 Plus program ‘DEG2RAD’ will convert this for you.