Complete a table from a graph

Learning Objectives Accurately identify the independent and dependent variables on a given graph. Extract specific data points (coordinates) from a graph representing a measurement relationship (e.g., volume vs. radius). Use the extracted data points to systematically complete a table of values. Interpolate values between plotted points on a continuous graph to estimate table entries. Extrapolate values beyond the plotted range of a graph to predict table entries, understanding the limitations. Analyze the relationship shown in the graph (e.g., linear, quadratic, trigonometric) to verify the completed table values. Apply the skill of completing a table from a graph to solve problems involving geometric measurements. Ever seen a graph showing a rocket's altitude over t...

TermDefinitionExample Coordinate Pair (x, y)A set of two numbers that locate a specific point on a Cartesian plane. The first number (x) is the horizontal position (independent variable), and the second (y) is the vertical position (dependent variable).On a graph of a circle's area vs. its radius, the point (3, 28.27) means a radius of 3 units corresponds to an area of approximately 28.27 square units. Independent VariableThe variable that is changed or controlled in an experiment or relationship, usually plotted on the horizontal x-axis.In a graph showing the volume of a sphere as its radius increases, the radius is the independent variable. Dependent VariableThe variable being measured, which 'depends' on the independent variable. It is usually plotted on the vertical y-a...

Coordinate Reading Principle For any point P(x, y) on the graph of a function f, the value of the function at x is y. That is, f(x) = y. To find a y-value for the table, locate the given x-value on the horizontal axis, move vertically to the graph's line or curve, and then move horizontally to read the corresponding y-value from the vertical axis. Volume of a Sphere (Example Measurement Formula) V = \frac{4}{3}\pi r^3 For a graph plotting the volume (V) of a sphere against its radius (r), the points (r, V) on the graph must satisfy this formula. This can be used to check the accuracy of the values you read from the graph. Pythagorean Theorem (in a graphical context) a^2 + b^2 = c^2 If a graph shows the relationship between the legs of a right triangle with a fix...