To complete the table with the colors of the graphs corresponding to the provided equations, we must analyze each function based on its characteristics, such as the type of function (linear, quadratic, or exponential), its behavior, and its shifts.
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Exponential Decay Functions:
- \( y = (3/4)^x - 3 \): This is an exponential decay function that decreases as \( x \) increases. The "-3" indicates a vertical shift downward by 3 units.
- \( y = (1.5)^x - 3 \): This is an exponential growth function, which increases as \( x \) increases, also shifting downward by 3 units.
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Linear Functions:
- \( y = -\frac{1}{2}x - 2 \): This is a linear function with a negative slope (-1/2), indicating that it goes down left to right, and it intersects the y-axis at -2.
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Quadratic Function:
- \( y = 0.1x^2 - 2 \): This is a quadratic function that opens upwards (since the coefficient 0.1 is positive) and has a vertical shift downward by 2 units.
To match these equations to the colors of their respective graphs, one would typically look at the provided graphs and then compare them with the characteristics outlined above.
Unfortunately, I don't have access to the specific graphs you're referring to, but you would take the following steps:
- Identify the graph that represents an exponential decay function, which will appear to start higher and decrease toward the horizontal asymptote.
- Locate the graph representing exponential growth, which will rise as you move from left to right.
- Find the linear graph, which will be a straight line with a negative slope.
- Identify the upward-opening parabola for the quadratic function.
Once you've matched the characteristics of each equation with the corresponding graph's behavior and color, fill in the table accordingly. If you can describe the graphs or provide their colors, I can help you match them more specifically!
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