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.

Responces:
nonlinear; function
nonlinear; not a function
linear; functuon
linear; not a function

1 answer

Based on the descriptions provided, here are the matches for each item:

  1. For the equation \(y = 3x^2 + 2\): This equation represents a nonlinear function (specifically a quadratic function).

  2. For the equation \(2x + 3y = 39\): This equation can be rearranged into the slope-intercept form \(y = \frac{39 - 2x}{3}\), which represents a linear function.

  3. For the table with X values (0, 1, 2, 3, 4) and corresponding Y values (1, 3, 9, 27, 81): This table shows an exponential relationship \(y = 3^x\) which can be classified as nonlinear and is indeed a function since each input has a unique output.

  4. For the graph that displays a parabola opening to the right with vertex at (-5, 0): This parabola represents a nonlinear function as well.

Given these points, the best response matches will be:

  • Equation \(y=3x^2 + 2\): nonlinear; function
  • Equation \(2x + 3y = 39\): linear; function
  • Exponential table: nonlinear; function
  • Parabolic graph: nonlinear; function

Therefore, the selected responses for the descriptions are:

  1. nonlinear; function for \(y = 3x^2 + 2\).
  2. linear; function for \(2x + 3y = 39\).
  3. nonlinear; function for the table with exponential values.
  4. nonlinear; function for the parabola.

Please ensure to select the appropriate responses for the items as described when filling in the input outputs.