Jefferson's scribe post - brief intro to logs

We were given questions as usual:


Sketch:

a) f(x) = sinx on the interval [-pi/2, pi/2]
*sketch a normal sine function to start.
since there was a domain given erase the graph so that the sine function is between -[pi/2 and pi/2]

a) g(x) = cosx on the interval [0, pi]

*pretty much the same as the top

c)h(x) = tanx on the interval [-pi/2, pi/2]


*and again the same steps apply here

next we were asked to sketch the inverse of the three graphs

a)

*draw the line of reflection y=x.
the coordinates change from (x,y) to (y,x) ei (2,3) to (3,2)
the original graph is just flipped over the line of reflection


b)


*same rules apply

c) *this one may be a little tricky
draw the line of reflection to start out with
since the graph is being reflected, so are the asymptotes
the asymptotes are now at x = 0 (orange)

Next we were asked to sketch:

y = 2^x

*the two most easy points you can get are when you input 0 and 1. If you replace x with 0 as an input you get an output (y coord) as 1. if you replace x with 1 as an input, then you get an output of 2



y = 3^x
next we had to sketch the inverse of the two :
*draw the line of reflection first. since the graph is being flipped over the line y = x, the asymptote(blue) is also being flipped.
*the new asymptote is at y = 0 (seen in red)
*if you forget the order of pairs (x,y) are flipped to (y,x)

y = 1/(2^x)
y = 1/(3^x)


when you input a number you nonetheless gt an output of the result. the inputs of these graphs are the exponents(x). And from the input you get an output of a power. IE 2^2(input/exponent) = 4(output/power)

Now when you do the inverse, the input is the power and the output is the exponent. it's basically saying it backwards, that's pretty much what an inverse is...sorta.



NOW it is time for me to bring in the logarithm aka the LOG(no not the tree log) . a log is a number but not any number. its a number that is formed from a result. An example Will come up later on this scribe post.


b^a=c

b = base
a = exponent
c = power


this is the basic formula for powers and exponents

a logarithm reverses that equation:

log_b(c) = a


this equation says that a logarithm is an EXPONENT!
you WILL i repeat WILL hear Mr k repeat this 100 times! because students will often forget about this

here's an example:

2³ = 8
log₂(8) = 3

*the 8 and 3 switch because a logarithm is an exponent.

heres another
5³ = 125

log₅125= 3



the next scribe will be.....jhoann