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Interpreting the graph

Alignments to Content Standards: F-IF.A


Use the graph (for example, by marking specific points) to illustrate the statements in (a)–(d). If possible, label the coordinates of any points you draw.


  1. $f(0) = 2$
  2. $f(−3)=f(3)=f(9)=0$
  3. $f(2) = g(2)$
  4. $g(x)>f(x)$ for $x>2$

IM Commentary

The purpose of this task is to help students learn to read information about a function from its graph, by asking them to show the part of the graph that exhibits a certain property of the function. The task could be used to further instruction on understanding functions, or as an assessment tool with the caveat that it requires some amount of creativity to decide how to best illustrate some of the statements.


  1. Cams_part_a_redo_214b379b2331a9022ddc15c7be3da9f6
  2. Cams_part_b_redo_e0e18c3aed264da28a6844214f2b1517
  3. Cams_part_c_redo_95d55e1e704dc3b9760fafccd6a350b8
  4. Cams_part_d_redo_4de59d14c093496d6b2350cf6d2fe53e

Heidi says:

over 2 years

Here is a link to a short TI-nspire document I made with a Geometry application in which the students may place points and labels to demonstrate their understanding of the function notation.


Cam says:

over 2 years

I'm not sure if this was intentional or not, but note that you have to request permission to access the document. Thanks for posting regardless!

Omar says:

about 4 years

I strongly support visualizing math. Lovely ideas. Perhaps moving in the other direction could be helpful. That is to say we give descriptions of some functions and let the great minds of the explorers draw the function/s.

Cam says:

about 4 years

Hi Explorers have to be given the time to construct their knowledge,

Thanks for your comment! Have you taken a look through the illustrations of F-IF.B.4? There are numerous tasks there which further connect the algebraic and graphical descriptions of functions, including tasks which encourage students to provide plausible sketches of functions themselves.