I assume you mean [itex]\displaystyle y=(-1)e^{-2x}\,,[/itex] 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:[itex]e^x[/itex] 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 [itex]\displaystyle y=(-1)e^{-2x}\,,[/itex] 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:[itex]\displaystyle y=e^{x}\,,[/itex]and[itex]\displaystyle y=\ln(x)\ ?[/itex]That's the place to start.
Then use what you've (hopefully) been learning about shifting, stretching, shrinking, flipping, etc. graphs.
The purpose of graphing functions is to visually represent the relationship between two or more variables. This allows us to better understand the behavior and patterns of the function and make predictions about its behavior in different scenarios.
The basic features of a function that can be identified on a graph include the x and y intercepts, the slope, the maximum and minimum points (if applicable), and any points of symmetry or discontinuity.
The domain of a function is the set of all possible input values, which can be determined by looking at the horizontal extent of the graph. The range of a function is the set of all possible output values, which can be determined by looking at the vertical extent of the graph.
A linear function has a constant rate of change, meaning its graph is a straight line. A non-linear function does not have a constant rate of change and its graph can take on various shapes, such as curves or loops. To identify them on a graph, you can look at the overall shape of the curve or use the slope formula to determine if the function is linear or non-linear.
Yes, a graph can be a useful tool in solving equations or finding the roots of a function. The x-intercepts of a function's graph represent the solutions to the equation y=0 and the points where the graph crosses the x-axis are the roots of the function. However, it is important to note that sometimes the roots may not be visible on the graph and other methods may be needed to find them.