Suppose you have a function f, of a variable X.
You select a value for X, say x. Calculate the value of f(x) that is, the value of the function when X takes that value x. Then, instead of writing the result in a table, mark the point [x, f(x)] on the coordinate plane. Repeat with other values for X and join up the points.
rule, table of values and graph
The graph of a continuous function will not have any 'breaks' or 'gaps' in it. You can draw it without lifting your pencil or pen. The graph of a discrete function will just be a set of lines.
To graph the inverse of a function without finding ordered pairs, you can reflect the original graph across the line ( y = x ). This is because the coordinates of the inverse function are the swapped coordinates of the original function. Thus, for every point ( (a, b) ) on the original graph, the point ( (b, a) ) will be on the graph of its inverse. Ensure that the original function is one-to-one for the inverse to be valid.
y=x+1
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.
rule, table of values and graph
The graph of a continuous function will not have any 'breaks' or 'gaps' in it. You can draw it without lifting your pencil or pen. The graph of a discrete function will just be a set of lines.
a graph where a function is described without using specific values
To graph the inverse of a function without finding ordered pairs, you can reflect the original graph across the line ( y = x ). This is because the coordinates of the inverse function are the swapped coordinates of the original function. Thus, for every point ( (a, b) ) on the original graph, the point ( (b, a) ) will be on the graph of its inverse. Ensure that the original function is one-to-one for the inverse to be valid.
Table Graph
y=x+1
You can use a table or a graph to organize you findings.
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.
In general you cannot. Any set of ordered pairs can be a graph, a table, a diagram or relation. Any set of ordered pairs that is one-to-one or many-to-one can be an equation, function.
Data is neither a table nor a graph, however, data may be presented in a table or depicted by a graph.
If you are looking at a graph and you want to know if a function is continuous, ask yourself this simple question: Can I trace the graph without lifting my pencil? If the answer is yes, then the function is continuous. That is, there should be no "jumps", "holes", or "asymptotes".
Input/output table, description in words, Equation, or some type of graph