Question

The function f(x) = x + is used to complete this table.

A 2-column table with 4 rows. The first column is labeled x with entries negative 1, 0, 1, 2. The second column is labeled f of x with entries 1, three-halves, 2, five-halves.

Which statements are true of the given function? Check all that apply.

fStartFraction negative 1 Over 2 EndFraction = –2
f(0) = three-halves
f(1) = –1
f(2) = 1
f(4) = seven-halves

Answer 1

From the table we get a linear rule f(x) = (1/2)x + 3/2 (since f(0)=3/2 and f(1)=2).

Evaluate each:

- f(-1/2) = (1/2)(-1/2)+3/2 = 5/4 ≠ -2 → false
- f(0) = 3/2 → true
- f(1) = 2 → false (not −1)
- f(2) = 5/2 → false (not 1)
- f(4) = (1/2)(4)+3/2 = 7/2 → true

So the true statements are: f(0) = 3/2 and f(4) = 7/2.