Question

assignment 6.2 graphs of exponential functions
score: 0/7 answered: 2/7
question 3
draw the graph of $f(x) = 3^x$
(grid provided)
clear all draw:
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Explanation:

Answer:

To draw the graph of \( f(x) = 3^x \), follow these steps:

Step 1: Identify Key Points

• When \( x = 0 \), \( f(0) = 3^0 = 1 \). So the point is \( (0, 1) \).
• When \( x = 1 \), \( f(1) = 3^1 = 3 \). So the point is \( (1, 3) \).
• When \( x = -1 \), \( f(-1) = 3^{-1} = \frac{1}{3} \approx 0.33 \). So the point is \( (-1, \frac{1}{3}) \).
• When \( x = 2 \), \( f(2) = 3^2 = 9 \). So the point is \( (2, 9) \).
• When \( x = -2 \), \( f(-2) = 3^{-2} = \frac{1}{9} \approx 0.11 \). So the point is \( (-2, \frac{1}{9}) \).

Step 2: Plot the Points

• Mark the points \( (0, 1) \), \( (1, 3) \), \( (-1, \frac{1}{3}) \), \( (2, 9) \), \( (-2, \frac{1}{9}) \) on the coordinate plane.

Step 3: Draw the Curve

• Since \( f(x) = 3^x \) is an exponential function with a base \( 3 > 1 \), the graph will be an increasing curve.
• Connect the plotted points smoothly, ensuring that as \( x \to -\infty \), the curve approaches the \( x \)-axis (since \( 3^x \to 0 \) as \( x \to -\infty \)) and as \( x \to \infty \), the curve rises rapidly.

The final graph should pass through the key points and have the characteristic shape of an exponential growth function.

(Note: Since this is a drawing task, the above steps guide you to plot the graph correctly. If you are using a graphing tool, input the function \( y = 3^x \) to generate the graph.)