rule, table of values and graph
To determine if a function represents a proportional relationship, you can use a table of values to check if the ratio of the output (y) to the input (x) remains constant. If the ratios are consistent, the relationship is proportional. Additionally, graphing the function will help you visualize the relationship; if the graph is a straight line that passes through the origin (0,0), then the function is proportional. If either the table or graph does not meet these criteria, the relationship is not proportional.
To graph a function on a coordinate plane, begin by creating a table of values by selecting input (x) values and calculating the corresponding output (y) values using the function. Plot each (x, y) point on the graph, marking the coordinates on the x-axis and y-axis. Once you have plotted enough points, connect them smoothly to visualize the function's shape. Finally, label the axes and the function for clarity.
To compare a linear function in a table to one represented as a graph, you can examine key characteristics such as the slope and y-intercept. In the table, the slope can be determined by calculating the change in y-values divided by the change in x-values between two points. On the graph, the slope is visually represented by the steepness of the line, while the y-intercept is the point where the line crosses the y-axis. Both representations should reflect the same linear relationship if they describe the same function.
I would set up a table of values and calculate several of the values of the variables (I would try to calculate the "interesting" values setting one to zero and calculating the other(s), guessing at a maximum or minimum value etc. Then I would plot the values on graph paper.
Make a table: for some different values of x, calculate the value of the function. Plot the points on a graph, and join them by lines.
rule, table of values and graph
use y = g(x) make a table of y values for several x values Find max/min values using derivative. graph the ordered pairs.
Depends what the graph is.
To determine if a function represents a proportional relationship, you can use a table of values to check if the ratio of the output (y) to the input (x) remains constant. If the ratios are consistent, the relationship is proportional. Additionally, graphing the function will help you visualize the relationship; if the graph is a straight line that passes through the origin (0,0), then the function is proportional. If either the table or graph does not meet these criteria, the relationship is not proportional.
A table you make to find the coordinates to graph.
To graph a function on a coordinate plane, begin by creating a table of values by selecting input (x) values and calculating the corresponding output (y) values using the function. Plot each (x, y) point on the graph, marking the coordinates on the x-axis and y-axis. Once you have plotted enough points, connect them smoothly to visualize the function's shape. Finally, label the axes and the function for clarity.
y = sin x, or y = cos x etc. can be graphed by making a table of values. The x column in the table would be angle measurements (usually in degrees or radians) and the y column would be the trig. function value. Then plot the points and sketch the curve going thru those points. Ex: for y = sin x x , y 0 0 30 0.5 45 0.707 etc and then graph these
Any explanation will depend on whether or not the table of values and the graph are related to one another. Nothing in the question indicates that they are.
To compare a linear function in a table to one represented as a graph, you can examine key characteristics such as the slope and y-intercept. In the table, the slope can be determined by calculating the change in y-values divided by the change in x-values between two points. On the graph, the slope is visually represented by the steepness of the line, while the y-intercept is the point where the line crosses the y-axis. Both representations should reflect the same linear relationship if they describe the same function.
I would set up a table of values and calculate several of the values of the variables (I would try to calculate the "interesting" values setting one to zero and calculating the other(s), guessing at a maximum or minimum value etc. Then I would plot the values on graph paper.
Which of the following is a disadvantage to using equations?