The vertical extent of the graph is all range values 5 and below,
This should be written as "The vertical extent of the graph is all range values from -infinity to 5, including 5..." The explanation just explains that you wrote it wrong and didn't bother to correct it.
If the function’s formula contains an even root, set the radicand greater than or equal to 0, and then solve.
So, that's not a fraction like the Howto describes.
solve for x
I see we've decided to exclusively list the input variable as x.
interval that is more than 0 and less than or equal to 100 and write (0,100].
it is worth noting that if x were the dependent variable for the amount of money spent, domain would be 0<x<=100.
Domain and Range
After learning that domain and range are related to the x and f(x) values of input of the dependent variable and output of the independent variable, I'm surprised to see that there's an entire section about it.
for any input, r, there is only one output, A.
should be written: for any input 'r', there is only one output 'A'. Comma castatstrophe. Use commas to set off extra information.
inputs q and r both give output n.
The original problem doesn't name inputs as 'q' and 'r', nor output 'n'.
Figures 1.1.1a and 1.1.1b.
a link here where I could open these up in a different browser tab would be useful here. I hate to have to leave my place in this online book and have to figure out where I left off when I get back. Better yet, it's an online text, why not just put the information here too. The original problem doesn't name inputs as 'q' and 'r', nor output 'n'.
To solve f(x)=4, we find the output value 4 on the vertical axis. Moving horizontally along the line y=4, we locate two points of the curve with output value 4: (−1,4) and (3,4). These points represent the two solutions to f(x)=4: −1 or 3. This means f(−1)=4 and f(3)=4, or when the input is −1 or 3, the output is 4. See Figure 1.1.9.
A good exercise here would be to come up with the equation of the graphed function. (x-1)^2=f(x) f(-1)=4 (-1,4), f(3)=4 (3,4)
How To: Given a function represented by a table, identify specific output and input values 1. Find the given input in the row (or column) of input values. 2. Identify the corresponding output value paired with that input value. 3. Find the given output values in the row (or column) of output values, noting every time that output value appears. 4. Identify the input value(s) corresponding to the given output value.
This information should have been included in the beginning table examples.
There is an urban legend that a goldfish has a memory of 3 seconds, but this is just a myth. Goldfish can remember up to 3 months, while the beta fish has a memory of up to 5 months. And while a puppy’s memory span is no longer than 30 seconds, the adult dog can remember for 5 minutes. This is meager compared to a cat, whose memory span lasts for 16 hours.
This information is clearly wrong.
Species - Typical Short‑Term Memory - Long‑Term Memory
Puppy Hours to days Months to years
Adult Dog Hours to days Months to years
Cat Hours to days Months to years
Goldfish Minutes to hours Months to years
Betta Fish Minutes to hours Weeks to months
Puppy 0.008 Adult Dog 0.083 Cat 3 Goldfish 2160 Beta Fish
This information is clearly wrong.
Species - Typical Short‑Term Memory - <br /> Long‑Term Memory
Puppy Hours to days <br /> Months to years
Adult Dog Hours to days <br /> Months to years
Cat Hours to days <br /> Months to years
Goldfish Minutes to hours <br /> Months to years
Betta Fish Minutes to hours <br /> Weeks to months
We can rewrite it to decide if p is a function of n.
A better description of how one would determine whether something is a function based on two variables that appear to be dependent on each other would make sense here. It would seem that they are functions of each other when written this way. Reference to the following example is not a factor in this statement.
and h(4)=24
Why am I finding h(4) in the solution?
With an input value of a+h, we must use the distributive property.
We could include here that f(a) is contained within the output of f(a+h) and substitute it to show that it =f(a)+h^2+2ah+3h
b. In this case, the input value is a letter so we cannot simplify the answer any further. f(a)=a2+3a−4
we can apply algebra and find that for (a+4)(a-1), a=1, -4
Table 1.1.5 displays the age of children in years and their corresponding heights.
It is unclear whether height could be a function of the age.