This discussion focuses on graphing the functions y=-e^(-2x) and y=ln(x-2)+1. The recommended x-range for the first function is from -2 to 5, while for the second function, it is from 2 to 10 due to its domain restrictions. Participants emphasize the importance of understanding the behavior of the exponential and logarithmic functions, particularly their rapid growth and domain limitations. Utilizing graphing calculators is suggested for quicker exploration of these functions.
PREREQUISITESStudents studying calculus, mathematics educators, and anyone looking to improve their skills in graphing functions and understanding their features.
I assume you mean \displaystyle y=(-1)e^{-2x}\,, which you could write as y = (e^(-2x))(-1), (the location of parentheses is important) or y = -e^(-2x), or better yet, y = -e-2x,zebra1707 said:Homework Statement
Hi there
I need assistance with two graphs that are causing me some problems
y=e(^-2x)(-1) and y=ln(x-2)+1
Homework Equations
I just need some guidance as to where to start - starting with a table - what range is appropriate?
The Attempt at a Solution
Stuck
HallsofIvy said:e^x goes to 0 very rapidly for x< 0 and goes up very rapidly for x> 0. I would recommend taking x from -1 or -2 to +4 or +5.
ln(x) is only defined for x> 0 so ln(x- 2) is only defined for x> 2. I would recommend taking x from 2 up to, say 10.
Wouldn't it have been faster to just play around with some numbers rather than wait for someone to respond here? Do you not have a graphing calculator? It would have taken only a few seconds to try various value on a calculator.
SammyS said:I assume you mean \displaystyle y=(-1)e^{-2x}\,, which you could write as y = (e^(-2x))(-1), (the location of parentheses is important) or y = -e^(-2x), or better yet, y = -e-2x,
and y = ln(x-2) + 1 .
Are you familiar with the graphs of:\displaystyle y=e^{x}\,,and\displaystyle y=\ln(x)\ ?That's the place to start.
Then use what you've (hopefully) been learning about shifting, stretching, shrinking, flipping, etc. graphs.