Two students evaluated functions with a given input and their work is shown below. One student is incorrect. Analyze their work to determine which student’s work is correct and describe the mistakes made.

Question

Two students evaluated functions with a given input and their work is shown below. One student is incorrect. Analyze their work to determine which student’s work is correct and describe the mistakes made.

Function Rule:
f(x)= 2 + 7

Student 1:
f(-1)= 2 + 7 (-1)
f(-1)= 9 (-1)
f(-1)= -9

Student 2:
f(-1)= 2 + 7 (-1)
f(-1)= 2-7
f(-1)= -5

Use the words input, output, order of operations, and function, in your explanation sentence.

Answer 1

The correct evaluation of the function with an input of -1 is given by Student 2. Student 1 made a mistake by incorrectly multiplying 7 with -1 instead of adding it to 2. This mistake violates the order of operations, where multiplication must be performed before addition. Therefore, the correct output for f(-1) is -5.