Question 1

So what's the difference between integer and real numbers?

Accepted Answer

Integers are just whole numbers, 1, 2, 3, 4, 5....-1, -2, and so on. Integers encompass all numbers that exist. Real numbers are crazy decimals, fractions, and whole numbers. You can think about integers as falling into the category of real numbers. Does that help?

Question 2

Why can't the interval of the domain be [0,15]?

Accepted Answer

On word problems, read, reread, and reread again.  it is easy to miss little details.  In the 1st sentence, it tells us that Mason is standing on the 5th step.  Then, in the end of the 2nd paragraph it tells us that if Mason moves down, then "n" will be a negative number.  The combination of these 2 pieces of info tell us that the 5th step = 0.  Since Mason can go down, the interval can't start at 0.  It needs to start at the lowest number that "n" can represent.  This would be the ground, where n = -5.  Thus, the interval is [-5, 10].
Hope this helps.

Question 3

I'm still kind of confused on how to find the interval and I have watched all videos about it. Could someone explain it to me?

Accepted Answer

The interval of the domain is a range of all the possible inputs that work in a function.  For example, if you walk to a hotdog stand containing 30 hotdogs that cost $1 each, your domain is how many possible inputs (hotdogs you can buy) work.  In this situation, the "interval" or "range of domains" is from 0 to 30.  You can't buy negative hotdogs so you cant go under 0, and you can't buy more than 30 hotdogs because that's all thats in stock.

This also works on a graph where the "x" value is your input and your "y" value is your output.  This means every point's x-value on the graph is a possible input and has a corresponding output which is it's y-value.  To find the range of domains, or interval of possible inputs, we must look at the range of valid x-values (because the x-values are the valid inputs).  This works so long as the graph is not infinite in the x-direction.  To find the interval, just look at how far the x-value reaches on each side, or the most negative input and most positive input.  You can also find the interval of outputs, or the "range" by finding how far up and down in the y-direction the graph goes.

Hope this helps!

Question 4

How is 0.5m pronounced? O.5 metres or 0.5 metre?

Accepted Answer

This is an oddity in math.  If you say 0.5, you would say point five meters, but if you have 1/2, you could say either one half meters or more often you may here one half of a meter.  meter (singular) is used with one meter, and in the second case of 1/2, it is used as a unit ratio.

Question 5

At 4:19, since the domain of the solution is all integers, is the range of the function be all real number because there is 0.5 meter?

Accepted Answer

The domain was not *all* integers as the ladder does not extend forever.  The domain is only integers from -5 up to 10 inclusive.
Yes, the range would need to be real numbers, but not all real numbers.  Again, it will be bounded  started at  h(-5) = 0 up to h(10) = 7.5.  A more accurate representation of range would be to create a set of specific values.   Since the steps increase by 0.5 meters, the range can't really be all real numbers from 0.5 to 7.5.  A more accurate range is the set = {0, 0.5; 1.0; 1.5; ... 6.5; 7.0; 7.5}

Question 6

SPOILER ALERT

In the video Sal indicates that steps are an integer because you can't have a part of one. But in one of the practice problems the input variable is a unit of time, specifically minutes. The hints explain that time is continuous so the domain should be real numbers. This however seems subjective when compared to the ladder problem as minutes are also a unit that isn't generally described in fractions as there are other units used (seconds) when describing parts of a minute. I get that this could be considered semantics but I'm curious if i'm missing something or if there is a hard rule in these situations or if it really matters at all and the concept is more important?

Accepted Answer

When you go up/down a ladder, you move one step at a time.  There are no 1/2 steps or 1/4 steps.  You can only move one step up or down.  This is why it is only defined for integers.

Time is measured in years, months, days, hours, minutes, seconds and fractions of seconds.  The units can be very small.  They are only limited by the precision of the device used to measure time.  Time does not have to be in minutes.  If something takes 1.5 minutes, we can and do use the fractional values.

Hope this helps you to see the difference.

Question 7

In what instances would you use parentheses instead of square brackets? I know parentheses do not include the value they are next to, but what would be an example of that?

Accepted Answer

So (0,1) means every value in between 0 and 1 but not including 1 and 0
[0,1] means every value in between 0 and 1 including 1 and 0
You'll see more applications of this in higher math levels I assume.

Question 8

at 3:54, why does he Sal say root 2 steps or pi steps when both aren't real nos. ?

Accepted Answer

Pi is a real number. It is not a rational number. But π along with √2 are real numbers.

Algebra 1

Course: Algebra 1 > Unit 8

Worked example: determining domain word problem (all integers)

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Video transcript