# Function Graph

Function Graph allows the student to choose a function and adjust two points on a four-quadrant grid. The student can adjust the dashed asymptote line for exponential and logarithmic graphs. The item author determines the number of cells in the symmetrical grid, axis values and titles, functionality of where points can snap to, and functions the student can choose from.

To create a Function Graph item, click Create Item and then the Elements tab. Under Response Interactions, click on the plus sign next to the label Function Graph in the left panel.

Note that at this time, Preview mode will not reflect any entered values or selections. Use the TN8 Preview button to see an accurate representation of the item.

### Grid

In this section of the Function Graph module, the item author defines the settings for the graph grid. The grid values and scale increments are all customizable. The scale for the default four quadrant grid goes from -5 to 5 along both *x* and *y* axes.

#### General

These settings allow you to define the size of a four quadrant grid. You can define the number of cells in a vertical column of the grid (Down), and the number of cells in a horizontal row of the grid (Across). The number of cells includes both quadrants that share the same axis.

*X*- and *Y*-Axis subsections

Scale Increment is a positive integer or decimal representing the difference in value between each vertical or horizontal gridline. For example, a scale increment of 5, creates gridlines labeled 0, 5, 10, etc. The default scale increment value for each axis is 1. This field must have a value to use the TN8 preview.

Highest Value is the greatest value on each axis; the right-most value on the *x*-axis and the top-most value on the *y*-axis. This is auto-generated using the values entered in Number of Cells Down and Across and Scale Increment. These values must be entered in order for the highest value to be calculated and displayed.

### Correct Response(s)

In this section of the Function Graph module, the item author enters information about the correct response.

#### Correct Function

In this subsection, the item author selects one correct function. Additional fields to enter correct response information will appear or disappear based on the function selected.

#### Equation Instructions

Equation Instructions are closed by default. Click the arrow to see sample equations as well as rules to enter equations correctly.

#### Equation

Enter the equation for the correct function in the format described under the equation instructions section. All student-plotted points must fit the defined equation for the response to be considered correct. An equation must be entered to view the item with the TN8 Preview.

#### Graph Values

All graph values should be entered at the same decimal place value that the TN8 Preview captures. You do not need to include trailing zeros. The best way to get this is to view the item with the TN8 Preview, place the points at the correct locations, and click “Get Score”. Copy the number(s) you see in the Variable RESPONSE (or RESPONSE_A, RESPONSE_B, etc.) into the appropriate field.

**Asymptote Value**: If the correct function is exponential or logarithmic, the item author must enter an asymptote value. This is the *y*-axis value of the asymptote for an exponential function is the x-axis value of the asymptote for a logarithmic function. It can be positive or negative, and a decimal. You do not need to include x= or y= before the value, and the interface will restrict you from doing so.

**Midline Value**: If the correct function is tangent/cotangent or sine/cosine, the item author must enter a midline value. The midline is the average of the *y* value of the maximum and the y value of the minimum of the function. This can be positive or negative, and a decimal. You do not need to include x= or y= before the value, and the interface will restrict you from doing so.

**Quarter Period Value**: If the correct function is tangent/cotangent or sine/cosine, the item author must enter a quarter period value. The quarter period is the absolute value of the difference between the *x* value of the midpoint and either the *x* value of the adjacent maximum or the *x* value of the adjacent minimum. This can be positive or negative, and a decimal. You do not need to include x= or y= before the value, and the interface will restrict you from doing so.

*Vertex Point: If the correct function is absolute value or quadratic, the item author must enter x and y coordinates for the vertex point of the function. They can be positive or negative, and a decimal.*

#### Sample Correct Coordinates

The item author should provide the *x* and *y* coordinates for two points. This is so publishing can validate that the correct answer is scoring correctly.