Question

fill in the table with the correct values for the graph of $f(x)=|x - 4|$. (fill each blank with an integer where the smaller integer is on the first blank.)

x	f(x)
3	1
4	(b)
(c)	1
6	(d)

(a) = \square (b) = \square (c) = \square (d) = \square

Explanation:

Step1: Solve for (a)

Set $|x-4|=2$. This gives $x-4=2$ or $x-4=-2$. Solving: $x=6$ or $x=2$. Choose the smaller integer, so $x=2$.

Step2: Solve for (b)

Substitute $x=4$: $f(4)=|4-4|=|0|=0$.

Step3: Solve for (c)

Set $|x-4|=1$. This gives $x-4=1$ or $x-4=-1$. Solving: $x=5$ or $x=3$. Choose the larger integer (since 3 is already used), so $x=5$.

Step4: Solve for (d)

Substitute $x=6$: $f(6)=|6-4|=|2|=2$.

Answer:

(a) = 2, (b) = 0, (c) = 5, (d) = 2