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The table below gives the value of the linear function f for several values of x. What is the value of a + b?

x 2 3 4
f(x) a 8 b

  1. 6
  2. 10
  3. 12
  4. None of the above
Explanation
Answer: D - The value of a + b is none of the listed answers. The value of a + b is 16.

Solution

Use the linear function equation.
f(x) = mx + b

1. When x = 3, 3m+b = 8. “Guess and check” values for m and b

When m = 2, b = 2

2. Find the missing outputs in the table

f(2) = 2(2) + 2 = 6

f(4) = 4(2) + 2 = 10

3. Add a + b

6 + 10 = 16
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