Hi again im trying to understand how to draw a graph from these,ive done them in the past but for the life of me i cant remember, i dont think they are to hard but any help would be great!!
y = 2e-x and y = x + 1 for -2 ≤ x ≤ 2
Hi again im trying to understand how to draw a graph from these,ive done them in the past but for the life of me i cant remember, i dont think they are to hard but any help would be great!!
y = 2e-x and y = x + 1 for -2 ≤ x ≤ 2
To learn how to graph linear functions (like the second function listed), try here.
To learn how to graph exponential functions (like the first function listed), try here.
To learn how to graph logarithmic functions (though none of that sort is listed in your post), try here.
It should be noted, however, that the graphing assumes that you are somewhat familiar with the underlying functions and equation types.
EDIT - I might be mistaken on your notation, I'm guessing you meant $\displaystyle y=2^{e-x}$ instead of $\displaystyle y=2e-x$. I'd recommend hitting up http://www.mathhelpforum.com/math-he...-tutorial.html , it makes these posts much clearer!
Let's rewrite these equations, as they are both linear equations of the form $\displaystyle y=mx+b$.]
$\displaystyle y=2e-x$
$\displaystyle y=-1x+2e$
Slope of $\displaystyle m=-1$, y-intercept at roughly $\displaystyle y=5.4365$
$\displaystyle
y=x+1
$
Slope of $\displaystyle m=1$, y-intercept at $\displaystyle y=1$.
These lines are straightforward to graph, just plot your y intercept, use your slope to find another point and make your line.
Use the inequality and only draw both lines on the domain $\displaystyle -2 \leq x \leq 2$, which basically means the lines don't continue to infinity, they have defined end-points at $\displaystyle x=-2$ and $\displaystyle x=2$. Does this help or would you like more clarification on anything?
Just to clarify, did you mean $\displaystyle y=2^{e-x}$ or $\displaystyle y=2e-x$.
Because the method that I posted does NOT work if the equation you are dealing with is $\displaystyle y=2^{e-x}$. The y-intercept shenanigans is only with the $\displaystyle y=mx+b$ linear equation format. Granted you can still find the y intercept of $\displaystyle y=2^{e-x}$ rather easily.
$\displaystyle y=2^{e-x}$
$\displaystyle y=2^{e-0}$
$\displaystyle y=2^e$
But the "find the y-intercept and use the slope to draw the line" technique will not work with $\displaystyle y=2^{e-x}$ because it is not a linear function, but an exponential function. The resource that stapel listed is great if that's the function you have.
Also, just as a personal technique, when I'm dealing with graphing linear equations, I like to make the scale of my graph 1 to 1, for example, for every 1 unit x, there is 1 unit y. Because this makes finding the slopes of your lines MUCH easier. Just remember $\displaystyle slope=\frac{rise}{run}$ and you can make points across a graph for a linear function in the blink of an eye.
hi,
Sorry if im not being clear,im not that great at this im learning, here is a copy and paste of the question.Thanks
7. (a) Draw by hand on graph paper, the graphs of
y = 2e-x and y = x + 1 for -2 ≤ x ≤ 2
(b) Hence solve the equation 2e-x - x = 1
Thanks for your patience
Don't be so hard on yourself, we've all had trouble with this at some point.
You're right on the axis, but remember that we aren't dealing with curves in THIS question, we are dealing with LINES. m is the slope of the line $\displaystyle slope=\frac{rise}{run}$ where rise is the change in y-value and run is the change in x-value.
Here is a quick sketch of the graph (Sorry for the crappy quality, i'm away from home, only got paint! :P ) Keep in mind this sketch does NOT include the restriction on x.
Gah, sorry. On the graph, note that the top line means to hit the y-axis at $\displaystyle y=2e$, and the bottom line should be hitting EXACTLY at $\displaystyle y=1$