Question

Given the function f(x) = | -2x + 4 |. Complete the table.

Answer 1

Answer:

See below.

Step-by-step explanation:

To complete the table, start by copying the given function.

f(x) = |-2x + 4|

Now let's start with the first line of the table: x = 6.

You are finding the value of function f when x = 6.

Replace x with 6 and evaluate the expression.

f(6) = |-2(6) + 4|

f(6) = |-12 + 4|

f(6) = |-8|

f(6) = 8

Second line of table:

x = -1

f(x) = |-2x + 4|

f(-1) = |-2(-1) + 4|

f(-1) = |2 + 4|

f(-1) = |6|

f(-1) = 6

For the third and fourth lines, you are given a y value, or the value of function f, and you are looking for x. Now you use the given value to set the function equal to, and you solve for x.

Line 3: f(x) = 4

f(x) = |-2x + 4|

|-2x + 4| = 4

-2x + 4 = 4   or   -2x + 4 = -4

-2x = 0   or   -2x = -8

x = 0    or   x = 4

Line 4: f(x) = 14

f(x) = |-2x + 4|

|-2x + 4| = 14

-2x + 4 = 14   or   -2x + 4 = -14

-2x = 10   or   -2x = -18

x = -5    or   x = 9

The table looks like this:

x          f(x)

6         8

-1         6

0,4      4

-5, 9     14

$\end{center}$