Use the graph to answer the question.

Question

What is equation shown in the graph?

(1 point)
Responses

y=2⋅(1.25)x
𝑦
=
2
⋅
(
1.25
)
𝑥
y is equal to 2 times 1 point 2 5 to the x th power

y=−2⋅(1.25)x
𝑦
=
−
2
⋅
(
1.25
)
𝑥
y is equal to negative 2 times 1 point 2 5 to the x th power

y=1.25⋅(2)x
𝑦
=
1.25
⋅
(
2
)
𝑥
y is equal to 1 point 2 5 times 2 to the x th power

y=2⋅−(1.25)x

Answer 1

To accurately identify the equation represented by the graph, I would need to see the graph itself or have information about its key features, such as its intercepts, slope, and whether it is increasing or decreasing.

However, I can help you understand how to determine the correct equation based on the information you'd observe in a graph.

1. Look for the Y-intercept: Is the graph starting at a positive or negative value when \(x = 0\)? This will help you determine if the coefficient in front of the equation is positive or negative.

2. Check the Growth/Decay: If the graph is increasing as \(x\) increases, the coefficient in front (if positive) indicates it is an exponential growth function. If it's decreasing, it indicates exponential decay.

3. Determine the Base: If the graph shows values that multiply by a value greater than 1 (like 1.25) as \(x\) increases, it suggests the base is larger than 1. If it decreases and the base is less than 1, this supports decay.

Given the options you provided:

• \(y = 2 \cdot (1.25)^x\) indicates exponential growth starting from 2.
• \(y = -2 \cdot (1.25)^x\) indicates growth starting from -2 but with a negative multiplier.
• \(y = 1.25 \cdot (2)^x\) indicates a different base and a different starting point.
• \(y = 2 \cdot -(1.25)^x\) indicates a negative causing the entire equation to decrease.

If you know whether the graph rises or falls and where it intersects the y-axis, that will help you select the right equation from the options provided. Without the graph, it's difficult to select the correct answer.

Answer 2

(-2, 1.28) (1, 2.5)

Answer 3

Based on the points you've provided, (-2, 1.28) and (1, 2.5), we can analyze them to determine which of the potential equations might best fit.

Analyzing the Points

1. Point (-2, 1.28): This point suggests that when \( x = -2 \), \( y \) is approximately 1.28.

2. Point (1, 2.5): This means that when \( x = 1 \), \( y \) is 2.5.

Understanding the Growth

Since the second point (1, 2.5) shows a value greater than the first point (-2, 1.28), it indicates that the graph is increasing as \( x \) moves from -2 to 1. This suggests that we are likely dealing with an exponential growth equation.

Testing the Options

1. Option: \( y = 2 \cdot (1.25)^x \)

   • When \( x = -2 \):
     \( y = 2 \cdot (1.25)^{-2} = 2 \cdot \frac{1}{(1.25)^2} \approx 2 \cdot 0.64 = 1.28 \)
     (This matches the first point.)
   • When \( x = 1 \):
     \( y = 2 \cdot (1.25)^1 = 2 \cdot 1.25 = 2.5 \)
     (This matches the second point.)

2. All other options won't satisfy both points as they either have different coefficients or their equations yield negative values or do not align with the provided points.

Conclusion

Based on the analysis of the points, the correct equation represented by the graph is:

\( y = 2 \cdot (1.25)^x \)

This is consistent with both provided points.