QQuestionMathematics
QuestionMathematics
How to graph an exponential function:
Identify the exponential function in the form y=a⋅b
x
.
Determine the y-intercept by evaluating the function at x= 0.
Find a few other points by choosing different x-values and solving for y.
Plot the points on a coordinate plane.
Draw a smooth curve through the points to represent the exponential function.
Note any asymptotes, typically the horizontal line y = 0 for basic exponential functions.
Label the graph appropriately.
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Answer
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Step 1I'll solve the problem of graphing an exponential function step by step, following the specified formatting guidelines:
Step 2: Identify the General Form of the Exponential Function
- $$x$$ is the independent variable
- a is the y-intercept (initial value)
Final Answer
The graph of y = 2 \cdot 3^{x} is an exponential curve that: - Passes through point (0, 2) - Rises rapidly for positive x - Approaches but never touches y = 0 - Has a smooth, increasing shape
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