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Graph this function.

y=3.5(2)x
Plot two points to graph the function.

1 answer

To graph the function \( y = 3.5(2)^x \), we will start by calculating a couple of points for different values of \( x \).

Step 1: Choose Values of \( x \)

Let's select two values for \( x \):

  1. \( x = 0 \)
  2. \( x = 1 \)

Step 2: Calculate Corresponding \( y \) Values

  1. For \( x = 0 \): \[ y = 3.5(2^0) = 3.5(1) = 3.5 \] So the point is \( (0, 3.5) \).

  2. For \( x = 1 \): \[ y = 3.5(2^1) = 3.5(2) = 7 \] So the point is \( (1, 7) \).

Step 3: Summary of Points

  • Point 1: \( (0, 3.5) \)
  • Point 2: \( (1, 7) \)

Step 4: Graph

To graph the function using these points:

  1. Plot the points:

    • Point \( (0, 3.5) \) is plotted above the x-axis at \( 3.5 \).
    • Point \( (1, 7) \) is plotted above the x-axis at \( 7 \).

  2. Draw the curve: Since this function is exponential (base 2) and multiplied by 3.5, the curve will rise rapidly as \( x \) increases.

The graph would show a quickly increasing curve, starting from the point \( (0, 3.5) \) and passing through \( (1, 7) \).

If you were to graph further values (like \( x = 2 \) or \( x = -1 \)), the curve would help in visualizing its behavior even more clearly.

Conclusion

These two points are sufficient to sketch a basic outline of the graph for the function \( y = 3.5(2^x) \). To see the full effect of its rapid growth, additional points can be calculated.