Name: Absolute value functions: solution walkthrough
Uploaded: 2026-11-13
Duration: 1 min 31 s
Description: The function f is defined by f(x) = 2|x + 1| - 5. What is the value of f(-4)? Try it, then watch the animated solution.

The graph of

f

is a V. Its lowest point is where

x + 1 = 0

: the vertex

({-1}, {-5})

.

Work inside the bars first:

{-4} + 1 = {-3}

, and

|{-3}| = 3

. That is how far

x = {-4}

is from the vertex.

Then the outside:

f({-4}) = 2 \cdot 3 - 5 = 6 - 5 = 1

. The V rises

6

from

y = {-5}

to

y = 1

.

Traps:

{-11}

drops the bars,

{-2}

forgets the

2

, and

5

makes

{-4}

positive before adding

1

.

Try it first