Match the correct description with the graph, table, and equation.(6 points)

Question

Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.

The image displays a graph and two tables representing mathematical functions.
Graph:
The graph shows a parabola opening to the right, with its vertex at (-1, 0). This indicates a quadratic function where x is expressed in terms of y.
Table 1:
This table presents a quadratic function. The y-values change at a non-constant rate, which is characteristic of a quadratic relationship.
Table 2:
This table represents an exponential function. The y-values are multiplied by a constant factor (3) as x increases by 1, demonstrating exponential growth.
The image effectively compares and contrasts different types of functions: quadratic (parabola and Table 1) and exponential (Table 2).
The image shows a graph of a cubic polynomial function, specifically f(x) = (x³ + 3x² - 6x - 8)/4. The graph is plotted on a Cartesian plane with the x-axis and y-axis labeled. The curve of the function passes through the points (-4, 0), (-1, 0) and (2, 0) on the x-axis, indicating these are the roots of the polynomial. The graph has a local maximum between x = -4 and x = -1, and a local minimum between x = -1 and x = 2. The grid lines on the graph provide a visual scale for the x and y values, ranging from -5 to 5 on both axes. The function's equation is displayed in the bottom right corner of the graph.
y=3x2+2
2x+3y=39

Responces:
Nonlinear; function
Nonlinear; not a function
Linear; function
Linear; not a function

Answer 1

To match the correct descriptions with the graph, tables, and equations provided, we can analyze the information step by step.

1. Graph Description:

   • The graph shows a parabola opening to the right, which indicates that it is a quadratic function. A quadratic function is nonlinear, and because it has only one output (y-value) for each input (x-value), it qualifies as a function.
   • Response: Nonlinear; function

2. Table 1:

   • The table presents a quadratic function with y-values changing at a non-constant rate, characteristic of a quadratic relationship. Since it represents a quadratic function, it is also nonlinear and a function.
   • Response: Nonlinear; function

3. Table 2:

   • The table represents an exponential function showing y-values multiplied by a constant factor as x increases. Exponential functions are also nonlinear but, like the previous examples, they satisfy the criteria of being a function.
   • Response: Nonlinear; function

4. Cubic Polynomial Function Description:

   • The graph description indicates that it is a cubic polynomial function characterized by the roots of the polynomial and local maxima/minima. Since cubic polynomials yield one output for each input, they are also classified as functions.
   • Response: Nonlinear; function

5. Equations:

   • y = 3x² + 2: This is a quadratic equation, which is nonlinear. It is also a function due to the definition of a function yielding a single output for each input.

   • Response: Nonlinear; function

   • 2x + 3y = 39: This is a linear equation because it can be expressed in the slope-intercept form (y = mx + b). It is also a function, as it can be rewritten in terms of y yielding a unique output for each input x.

   • Response: Linear; function

Final Matching:

1. Graph: Nonlinear; function
2. Table 1: Nonlinear; function
3. Table 2: Nonlinear; function
4. Equation y = 3x² + 2: Nonlinear; function
5. Equation 2x + 3y = 39: Linear; function

If you have a specific table or equation to assign later, please use the corresponding responses above.