Mathematics
Grade 11
15 min
Complete a table for a function graph
Complete a table for a function graph
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1
Introduction & Learning Objectives
Learning Objectives
Identify corresponding y-values for given x-values on a function graph.
Identify all corresponding x-values for a given y-value, recognizing when multiple solutions exist.
Determine the coordinates of key features like intercepts, maxima, and minima directly from a graph and record them in a table.
Accurately estimate function values for points that lie between grid lines on a graph.
Complete a table of values for complex functions (e.g., logarithmic, polynomial, or piecewise) by reading their graphs.
By the end of of this lesson, students will be able to analyze the behavior of a function, such as increasing/decreasing intervals, by creating a table of values from its graph.
Ever seen a complex scientific graph and wondered how to pull specific data poin...
2
Key Concepts & Vocabulary
TermDefinitionExample
Function GraphA visual representation of a function on a coordinate plane, where each point (x, y) on the graph satisfies the equation y = f(x).The graph of a parabola represents the function f(x) = x². The point (3, 9) is on the graph because f(3) = 3² = 9.
Coordinate Pair (Ordered Pair)A pair of numbers (x, y) that specifies a unique point on a Cartesian coordinate plane. The first number is the x-coordinate (horizontal position), and the second is the y-coordinate (vertical position).In the coordinate pair (-2, 5), the x-value is -2 and the y-value is 5.
Function NotationA way to represent the output value (y-value) of a function for a given input value (x-value). f(x) is read as 'f of x' and is equivalent to y.If a graph contains the point (4, 7), we ca...
3
Core Formulas
Finding an Output (y-value)
Given x = a, find y = f(a)
To find the function's value for a given x-coordinate 'a', locate 'a' on the x-axis. Move vertically (up or down) until you intersect the function's graph. Then, move horizontally from that point to the y-axis to read the corresponding y-value.
Finding an Input (x-value)
Given y = b, find x such that f(x) = b
To find the x-value(s) that produce a given y-value 'b', locate 'b' on the y-axis. Move horizontally (left or right) across the graph. For every point where you intersect the function's graph, move vertically (up or down) to the x-axis to read the corresponding x-value. Note that there may be zero, one, or multiple solutions.
4 more steps in this tutorial
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Challenging
A table is being created from the graph of a function f(x). The table needs to show the coordinates of the local maximum and the value of x where f(x) = -5. The graph shows a local maximum at (-2, 4) and the line y = -5 intersects the graph at x = 3. Which table correctly shows this information?
A.| x | f(x) |
|---|---|
| -2 | 4 |
| -5 | 3 |
B.| x | f(x) |
|---|---|
| 4 | -2 |
| 3 | -5 |
C.| x | f(x) |
|---|---|
| -2 | 4 |
| 3 | -5 |
D.| x | f(x) |
|---|---|
| -2 | Max |
| 3 | -5 |
Challenging
The graph of a function g(x) is shown. By creating a table of its key features (intercepts and extrema), determine the approximate interval on which the function is both positive (g(x) > 0) and increasing.
A.From the y-intercept to the local maximum.
B.From the local minimum to the second x-intercept.
C.From the first x-intercept to the local maximum.
D.From the local maximum to the second x-intercept.
Challenging
The graph of y = |x² - 9| is shown. It is a 'W' shape with x-intercepts at -3 and 3, a y-intercept at 9, and a local minimum at (0,0) reflected to a local maximum at (0,9). It has sharp corners (cusps) at (-3, 0) and (3, 0). Which table incorrectly represents a point on this graph?
A.| x | y |
|---|---|
| -3 | 0 |
B.| x | y |
|---|---|
| 0 | 9 |
C.| x | y |
|---|---|
| 4 | 7 |
D.| x | y |
|---|---|
| 2 | -5 |
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