The exponential function which represent the graph shown in image is f(x)=2.(1/4)ˣ. Option C is correct.
What is an exponential function?
Exponential function is the function in which the function growth or decay with the power of the independent variable. The curve of the exponential function depends on the value of its variable.
The exponential function with dependent variable y and independent variable x can be written as,
f(x)=a.bˣ
Here, x is the variable in the power of a number, b is a constant which is known as the change factor and a is the initial value of the function.
Here, in the graph, it passes from the (0,2) and (2,0) from x and y axis. it tells us that the initial value of is 2.
a=2
The graph is plotted on right side in opposite way, which tells the value of b is in the reciprocal. Thus,
b=1/4.
Put the values as,
f(x)=a.bˣ
f(x)=2.(1/4)ˣ
Hence, the exponential function which represent the graph shown in image is f(x)=2.(1/4)ˣ. Option C is correct.
Learn more about the exponential function here;
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