0
votes
1answer
17 views

find exponential line going through 3 points

I have 3 points:(0,0);(55,64);(137,200) How could i get the formula going through those 3 points? They line up in an exponential line like this one:
0
votes
1answer
31 views

Sketching the graph of $y =\ln(4-x)$

$y = \ln(4 - x) $ This graph has two operations applied to the $\ln x$ graph - a reflection and a translation. If you reflect the graph in the $y$-axis first, and then shift the graph 4 units to ...
1
vote
2answers
22 views

How do I find the inverse of this exponential function?

$x=-3(3^{-x})+9$ I know the steps up until a certain point. $x=-3(3^{-y})+9$ $x-9=-3(3^{-y})$ $\frac{(x-9)}{-3} = 3^y$ $ln (\frac{x-9}{-3}) = -y * ln 3$ Not sure what to do from here. I know I ...
1
vote
1answer
26 views

Sketching Logs with Quadratic Terms

$\log(x^2+1) = y$ asymptote at $x^2+1 > 0$ and so there is no asymptote $x$ and $y$ intercept at $(0,0)$ How do you know that the function goes both directions, and has a dip in the middle? ...
0
votes
1answer
66 views

Steps to Graph Exponential Equations & Absolute Value

how to sketch: $-e^{|-x-1|} + 2$ Can someone clarify: $|f(x)|:$ we draw $f(x)$ and then reflect the ($-y$ parts) in the $x$-axis $f|(x)|:$ we draw $f(x)$ and then reflect the ($-x$ parts) in the ...
0
votes
3answers
433 views

“Linearize” an exponential-looking graph with log function

This may be a beginner question, but I can't quite wrap my head around logs... I have a set of data (from an experiment) which gives me an exponential-looking graph (Fig 1). I'd like to "linearize" ...
1
vote
1answer
96 views

(Basic High School Mathematics) Graphing the inverse square law

I did an experiment measuring the intensity of light in relation to the distance away from a source. How would I graph the avg intensity over 1/distance squared? Note that T1 = trial 1 etc.. It's ...
3
votes
1answer
163 views

How can we describe the graph of $x^x$ for negative values?

We usually only see the graph $y=x^x$ for $x>0$, because $x^x$ is a complex number for most negative values of $x$. Yet here is a full graph of $y=x^x$ on the real line: This graph may seem like ...
0
votes
3answers
26 views

What constrains the following functional equation of exponents?

If I am not incorrect,the standard (Is it he standard?) form of an exponential equation is $$y=ab^{x-h}+k$$ What are the constraints on this equation, or in other words, how do each of the variables ...
0
votes
1answer
106 views

Finding the Y axis value on a exponential trendline (MS Office Excel)

Hello I'm having some problems finding out the correct equation, or if there is one, to find the value on the Y axis. I have the following values: ...
1
vote
1answer
55 views

Graph of $y=x^x$ for $x<0$

I have been wondering about the graph of $y=x^x$. Most graphing calculators will quite happily graph it up to $0$, but after that they don't do anything else. Basic calculation suggests that, while ...
2
votes
4answers
184 views

Fitting curve for exponential: $y = A - B\mathrm{e}^{-t/\tau}$

I have some data that follows a saturation or charging profile such as $y = A - B\mathrm{e}^{-t/\tau}$. To begin with, is there a proper name for this function? I have seen it many times, including: ...
0
votes
2answers
55 views

Creating a custom exponential function

I'm trying to come up with an exponential function that starts at zero, rises quickly (in $y$) between $x = 0$ and $x = 100$ and then slowly levels off as $x$ continues into infinity. Something that ...
0
votes
1answer
112 views

Finding the equation of the graph y=a^x +b from given points (2,5) and (0,-4)

I am trying to figure out the equation of an exponential graph from two given points. I know you have to plug each set of points into the equation, but I forget exactly how to solve this. As stated ...
0
votes
2answers
453 views

Finding exact values of $A$ and $B$ from exponential point on graph?

I am faced with a problem that I cannot seem to solve. Here it is: The graph $y = a^x + b$ is shown below, find the EXACT values of $a$ and $b$. The graph is an exponential graph, it has a ...
0
votes
2answers
83 views

What is the simplest $\Bbb{R}\to\Bbb{R}$ function with two peaks and a valley?

What is the simplest $\Bbb{R}\to\Bbb{R}$ function with two peaks and a valley? I have a set of points in $\Bbb{R^2}$ and I would like to fit a curve to the points, the points approximately lie on a ...
0
votes
2answers
60 views

Finding the inverse of $y= 100(1-0.9^t)$

I must solve the inverse of this function $y= 100(1-0.9^t)$ as I solve? I try but the equation $\ln$ left with negative logarithm.
1
vote
1answer
55 views

What changes in a graph when modifying a in $ae^x$

What happens in a graph when you modify the value of $a$ in the following equation: $ae^x$ where e is the natural number. At first it seemed like it was translating the graph horizontally but when ...
1
vote
1answer
489 views

Normalizing an exponential function

Given the equation $a^\frac yx + a^x=b$ is there a way to normalize this function into a form where $y=$...? In short can I express $y$ in terms of $x$ if $a$ and $b$ are constants?
0
votes
3answers
77 views

Why does the graph of $x^n$ only have an imaginary component if $n$ is not an integer?

I was playing around graphing equations and noticed that only non-integer exponents of x yield imaginary graphs. Try it on Wolfram Alpha. Why is that?
3
votes
1answer
147 views

Can the graph of $x^x$ have a real-valued plot below zero?

The function $f(x) = x^x$ gives a complex number only if x has an even denominator. I'm not sure about irrational numbers. Why, then, is the best graph I can find of that function that of Wolfram ...