Student *A* and student *B* were given the following graph and asked to find the value of 

*f*(*x*)

 when 

*x* = 1.

 Student *A* gave an answer of 0 while student *B* gave an answer of −6. Who is incorrect? Drag and drop the correct option into each box to complete the explanation of the error.
 

 
Student  is incorrect. The student started at  on the *y*-axis, did not need to move horizontally to get to the graph, and so moved  to  on the *x*-axis. The student should have started at  on the *x*-axis, moved  to the graph, and then moved  to  on the *y*-axis, which is what student  did.


 1 

 0 

 horizontally 

 -6 

 A 

 vertically 

 B 

 A 

 A 

 1 

 1 

 vertically 

 vertically 

 0 

 0 

 horizontally 

 horizontally 

 B 

 B 

 -6 

 -6 

The correct explanation for the error is as follows:

**Student A is incorrect.** The student started at **1** on the *y*-axis, did not need to move **horizontally** to get to the graph, and so moved **vertically** to **0** on the *x*-axis. The student should have started at **1** on the *x*-axis, moved **vertically** to the graph, and then moved **horizontally** to **-6** on the *y*-axis, which is what student **B** did.**

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Would you like further details or have any other questions?

Here are 5 related questions for practice:
1. How do you interpret the *x*- and *y*-axis values in function graphs?
2. How can you determine *f(x)* from a graph when *x* is given?
3. What is the significance of horizontal vs. vertical movements on a function graph?
4. What does *f(1)* represent on the graph of a function?
5. What common mistakes might occur when reading function values from graphs?

**Tip:** Always ensure you start by locating the correct *x*-value before determining the corresponding *y*-value on a function graph.

Student A and student B were given the following graph and asked to find the value of f(x) when x = 1. Student A gave an answer of 0 while student B gave an answer of −6. Who is incorrect? Drag and drop the correct option into each box to complete the explanation of the error.

This problem helps students identify common errors when evaluating functions from graphs. The solution involves understanding function graphs, locating points based on x-values, and moving vertically and horizontally on the graph. Suitable for students in Grades 8-10.

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