Question

Can someone please help with this project? I have to describe the graph and I don't know what to say! Medal, fan, and testimonial for quick, accurate responses!

Answer 1

these are the exact instructions

Answer 2

try thinking about these:

where does it start? where does it end?

does the graph exist everywhere? as in all the four quadrants?

what is its trend? as in does it increase as x increases? or does it decrease?

Answer 3

@emmagrace231 what are your thoughts on the points i mentioned?

Answer 4

you should talk about the following:
1) domain and range (if possible)
2) x and y intercepts
3) symmetry (even/odd function) or periodicity
4) Whether the function is increasing or decreasing
5) Any critical points, maxima/minima.
6) Any asymptotes or limiting values

Only talk about what is visible on the graph or inherent in its equation.

Answer 5

so in this example, 1) 2) 4) and 5) would be a good set of descriptors

Answer 6

how do i show/ find all of this?! @mww

Answer 7

@baru

Answer 8

1)domain: what is the of set permissible x values on the graph (or that would can sub into y = sqrt(x)? Here you should find your graph only makes sense for x greater than or equal to 0 since you can only take a sqrt of zero or positive numbers for real x. (also that the graph is confined to the right of x = 0)

range: what are the set of possible y values that come out as a result?
2) x and y intercepts (i.e where does the graph touch the x or y axes?): Let x = 0 to find y intercept, and let y = 0 to find x intercept
3) f(x) = f(-x) implies even function, -f(x) = f(-x) implies an odd function, otherwise neither.
4) If f'(x) > 0 for an interval, it is increasing over that interval. Otherwise if f'(x) < 0 it is decreasing over the interval.
5) Critical pts: are there endpoints iof the domain on the graph, or vertical tangents where f'(x) is undefined? Are there pts where f'(x) = 0 to give you maxima/minima, or inflexions?
6) Asymptotes: Does f(x) --> infinity or -infinity for certain values of x? (vertical asymptote)
Does f(x) tend towards a finite number L where x --> infinity or - infinity? (horizontal asymptote)
Does f(x) --> g(x) when x --> infinity or 0 infinity (oblique asymptote)