Writing the equation of a transformed exp function given the graph

In summary, the conversation discusses the transformation of the exponential function f(x) = 2^x and how to write an equation for it. The graph in question is graph B and there are concerns about solving for the variables involved, including k, a, and d. The value of c is known to be 0 as it is the asymptote. The speaker requests assistance in finding a solution to the problem.
  • #1
needingtoknow
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Homework Statement



EXPONENTIAL FUNCTION

The graph represents a transformation of the function f(x) = 2^x, Write an equation for it.

The graph in question is the second one, graph B.

http://ars.els-cdn.com/content/image/1-s2.0-S0006349598778683-gr1.gif

Since there are more variables involved I am not sure how to solve. I know if its just ab^x then I can find two points and do a system of equations. But what is the process when I have, k, a, d variables to worry about as well. I know that c is 0 because its the asymptote. Can someone please help. Thanks!
 
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  • #2
There's no way to solve this as a completely open-ended question. You have to make some assumption about the general form of the transformation. Suggest something.
 

Related to Writing the equation of a transformed exp function given the graph

1. What is an exponential function?

An exponential function is a mathematical function in the form of f(x) = a^x, where a is a constant and x is the variable. It is characterized by a rapid increase in value as x increases.

2. How do you identify a transformed exponential function from a graph?

A transformed exponential function can be identified by observing changes in the graph, such as shifts in the y-intercept or changes in the slope. These changes indicate that the function has been transformed from its original form.

3. What are the key components of an exponential function equation?

The key components of an exponential function equation are the base (a), the exponent (x), and the y-intercept (b). The base determines the rate of growth or decay, the exponent represents the input variable, and the y-intercept is the starting value of the function.

4. How do you write the equation of a transformed exponential function given the graph?

To write the equation of a transformed exponential function, you need to identify the values of the base (a), the exponent (x), and the y-intercept (b) from the given graph. Then, plug these values into the general form of an exponential function, f(x) = a^x + b, to obtain the specific equation for the transformed function.

5. What is the purpose of transforming an exponential function?

The purpose of transforming an exponential function is to change its characteristics, such as the rate of growth or decay, to better fit a given situation or set of data. This allows for more accurate predictions and analysis of real-world phenomena.

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