Plot the function y = 3 * 2^x on the provided grid.
Understand the Problem
The question asks to plot the exponential function y = 3 * 2^x on the provided grid.
Answer
Plot the points $(-2, 0.75)$, $(-1, 1.5)$, $(0, 3)$, $(1, 6)$, and $(2, 12)$ and draw a smooth curve through them to represent $y = 3 \cdot 2^x$.
Answer for screen readers
The points to plot are: $(-2, 0.75)$, $(-1, 1.5)$, $(0, 3)$, $(1, 6)$, $(2, 12)$
Steps to Solve
- Choose x values
Select a few values for $x$ to calculate the corresponding $y$ values. A good choice of $x$ values would be -2, -1, 0, 1, and 2.
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Calculate y values for chosen x values Substitute the chosen x values into the equation $y = 3 \cdot 2^x$.
- For $x = -2$: $y = 3 \cdot 2^{-2} = 3 \cdot \frac{1}{4} = \frac{3}{4} = 0.75$
- For $x = -1$: $y = 3 \cdot 2^{-1} = 3 \cdot \frac{1}{2} = \frac{3}{2} = 1.5$
- For $x = 0$: $y = 3 \cdot 2^{0} = 3 \cdot 1 = 3$
- For $x = 1$: $y = 3 \cdot 2^{1} = 3 \cdot 2 = 6$
- For $x = 2$: $y = 3 \cdot 2^{2} = 3 \cdot 4 = 12$
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Plot the points Plot the points (-2, 0.75), (-1, 1.5), (0, 3), (1, 6), and (2, 12) on the grid.
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Draw the curve Draw a smooth exponential curve through the plotted points. The curve should approach the x-axis as x becomes a large negative number and increase sharply as x increases.
The points to plot are: $(-2, 0.75)$, $(-1, 1.5)$, $(0, 3)$, $(1, 6)$, $(2, 12)$
More Information
Exponential functions of the form $y = a \cdot b^x$ where $b > 1$ grow very rapidly as $x$ increases.
Tips
A common mistake is to miscalculate the y values, especially when dealing with negative exponents. For example, $2^{-2}$ is often mistaken as -4 instead of $\frac{1}{4}$. Another mistake is to plot the points incorrectly on the grid. Lastly, students may try to connect the points with straight lines which is incorrect, as this is an exponential function and should be represented by a smooth curve.
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