Ask a New Question
Menu

Match the graph, table, and equation with the correct description.

(6 points)
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.

y=3x2+2

2x+3y=39

The image shows a table with two columns labeled "X" and "Y". The table presents a set of paired values, where the "X" values are 0, 1, 2, 3, and 4, and the corresponding "Y" values are 1, 3, 9, 27, and 81. This set of data represents an exponential function, specifically y = 3^x, where each Y value is obtained by raising 3 to the power of the corresponding X value. This type of table is often used in mathematics to illustrate the relationship between input and output values for a given function.

he image displays a graph of a polynomial function along with a table of values. The graph is a curve that extends from the bottom left, rises to a local maximum, descends to a local minimum, and then rises sharply to the upper right. It is plotted on a Cartesian coordinate system with labeled x and y axes. The equation for the function is written as f(x) = x³ + x² - 3x - 1. The table of values provides specific points on the graph:
x
y
-2
-7
-1
-4
0
-1
1
2
2
5

The image shows a graph of a parabola opening to the right. The graph is plotted on a Cartesian coordinate system with the x-axis and y-axis labeled. The parabola's vertex is at (-5, 0), and it extends towards the positive x-axis. The equation of this parabola is likely in the form x = ay^2 + c, where 'a' is a positive constant and 'c' is -5. The graph spans from approximately x = -5 to x = 6 and y = -3 to y = 3. The text labels on the axes indicate values from -6 to 6 for both x and y.

These points correspond to the curve's position on the graph. For example, when x is -2, y is -7, and when x is 1, y is 2. The graph and the table of values visually and numerically represent the same cubic function, showing how the y-values change in response to the x-values. Polynomial functions are commonly used in mathematics to model various relationships and are characterized by their smooth, continuous curves.

1 answer

To match the graph, table, and equation with their correct descriptions, we can analyze each piece of information provided:

  1. Equation: y = 3x² + 2

    • This is a quadratic equation, which describes a parabola that opens upward.

  2. Equation: 2x + 3y = 39

    • This is a linear equation in standard form that describes a straight line.

  3. Table of values:

    • The table lists values where X: 0, 1, 2, 3, and 4 correspond to Y: 1, 3, 9, 27, and 81. The relationship is exponential, specifically y = 3^x.

  4. Graph of a polynomial function (f(x) = x³ + x² - 3x - 1):

    • The description matches the behavior of a cubic function, characterized by the curve with local extremities.

  5. Graph of a parabola opening to the right:

    • This graph matches the parabola described in the equation form x = ay² + c, suggesting that the parabola opens to the right.

Now, here’s the appropriate matching:

  • y = 3x² + 2 → The parabola opening upward.
  • 2x + 3y = 39 → The straight line (though no direct description for it was provided, it fits with the linear nature).
  • Table (X: 0, 1, 2, 3, 4 and Y: 1, 3, 9, 27, 81) → Exponential function, y = 3^x.
  • Graph (f(x) = x³ + x² - 3x - 1) → Describes the cubic function.
  • Graph of a parabola opening to the right → Relevant parabola described as x = ay² + c.

So the matches are as follows:

  • y = 3x² + 2 → Parabola opening upward
  • 2x + 3y = 39 → Linear equation (description inferred)
  • Table values with exponential function → y = 3^x
  • f(x) = x³ + x² - 3x - 1 → Graph of cubic function
  • Parabola opening to the right → Corresponds with the parabola form equation.

In case you need them neatly grouped:

  • Quadratic Equation (y = 3x² + 2): Corresponds to parabola.
  • Linear Equation (2x + 3y = 39): Corresponds to linear relationship.
  • Exponential Table of values: y = 3^x.
  • Cubic Function (f(x) = x³ + x² - 3x - 1): Graph of polynomial function.
  • Right-opening Parabola: Form of x = ay² + c.

This proper matching provides clarity on each graph, table, and equation associated with their respective descriptions.