Question

The graph of an exponential function is given. Select the function for each graph from the given options.
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Part 1
Drag each function given above into the area below the appropriate​ graph, depending on which function is represented by which graph.
19.
-3
3
-10
2
x
y



A coordinate system has a horizontal x-axis labeled from negative 3 to 3 in increments of 0.5 and a vertical y-axis labeled from negative 10 to 2 in increments of 1. From left to right, a curve rises steeply in quadrant 3 passing through (negative 2, negative 9) and (negative 1, negative 3), crosses the y-axis at (0, negative 1), and then rises shallowly in quadrant 4 passing through approximately (1, negative one third). As x increases towards positive infinity, the curve approaches the positive x-axis from below.
20.
-3
3
-2
10
x
y



A coordinate system has a horizontal x-axis labeled from negative 3 to 3 in increments of 0.5 and a vertical y-axis labeled from negative 2 to 10 in increments of 1. From left to right, a curve rises shallowly in quadrant 2 passing through (negative 1, one ninth) and crosses the y-axis at (0, one third), and then rises steeply in quadrant 1 passing through approximately (1, 1); (2, 3); and (3, 9). As x decreases towards negative infinity, the curve approaches the negative x-axis from above.
21.
-3
3
-10
2
x
y



A coordinate system has a horizontal x-axis labeled from negative 3 to 3 in increments of 0.5 and a vertical y-axis labeled from negative 10 to 2 in increments of 1. From left to right, a curve falls shallowly in quadrant 3 passing through (negative 1, negative one third), crosses the y-axis at (0, negative 1), and then falls steeply in quadrant 4 passing through approximately (1, negative 3) and (2, negative 9). As x decreases towards negative infinity, the curve approaches the negative x-axis from below.
22.
-3
3
-2
10
x
y



A coordinate system has a horizontal x-axis labeled from negative 3 to 3 in increments of 0.5 and a vertical y-axis labeled from negative 2 to 10 in increments of 1. From left to right, a curve rises shallowly in quadrant 2 passing through (negative 1, one third), crosses the y-axis at (0, 1), and then rises steeply in quadrant 1 passing through approximately (1, 3) and (2, 9). As x decreases towards negative infinity, the curve approaches the negative x-axis from above.
23.
-3
3
-2
10
x
y



A coordinate system has a horizontal x-axis labeled from negative 3 to 3 in increments of 0.5 and a vertical y-axis labeled from negative 2 to 10 in increments of 1. From left to right, a curve rises shallowly in quadrant 3, crosses the y-axis at (0, 0), and then rises steeply in quadrant 1 passing through approximately (1, 2) and (2, 8). As x decreases towards negative infinity, the curve approaches the line y = negative 1 from above.
24.
-3
3
-2
10
x
y



A coordinate system has a horizontal x-axis labeled from negative 3 to 3 in increments of 0.5 and a vertical y-axis labeled from negative 2 to 10 in increments of 1. From left to right, a curve falls steeply in quadrant 2 passing through (negative 2, 9) and (negative 1, 3), crosses the y-axis at (0, 1), and then falls shallowly in quadrant 1 passing through approximately (1, one third). As x increases towards positive infinity, the curve approaches the positive x-axis from above.

Answers

GPT-4o mini
Based on the descriptions provided for each graph, I will match them with the most likely corresponding exponential functions.

1. **Graph 1** (Rises steeply, crosses y-axis at (0, -1)):
- This graph has a horizontal asymptote (y = 0) and rises steeply in the negative quadrant suggesting a function like \(y = a \cdot b^{x}\) where \(b > 1\). The negative y-values indicate \(b < 0\) situation.
- **Possible function: \(y = -\frac{1}{3} \cdot 2^x\)** or similar.

2. **Graph 2** (Rises shallowly, crossing y-axis at (0, 1/3)):
- This graph also has a horizontal asymptote and rises steeply in quadrant 1. It starts from positive values linear to the x-axis, suggesting an exponential growth function.
- **Possible function: \( y = \frac{1}{3} \cdot 3^x \)** or similar.

3. **Graph 3** (Falls shallowly in quadrant 3, crosses y-axis at (0, -1)):
- This graph indicates decay and negative values. The steep descent suggests something similar to a decay function.
- **Possible function: \( y = -3^x \)** or similar.

4. **Graph 4** (Rises, crosses y-axis at (0, 1)):
- This graph rises from the y-axis at 1 and suggests a positive exponential growth.
- **Possible function: \( y = 2^x \)** or similar.

5. **Graph 5** (Rises shallowly, crosses y-axis at (0, 0)):
- This graph starts from (0, 0), hinting at an exponential function that begins close to zero.
- **Possible function: \( y = 2^x - 1 \)** or similar.

6. **Graph 6** (Falls steeply, crossing y-axis at (0, 1)):
- This graph falls steeply from above the x-axis. It indicates a decay function.
- **Possible function: \( y = 3^{-x}\)** or similar.

Based on the descriptions and correlations to what an exponential graph's behavior is, you can use the integral properties (values and asymptotes) given to deduce the matching functions to their respective graphs. However, if you provide the explicit functions available, I can better determine which function matches which graph.

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