Question

Which function is represented by the graph? f(x) = â’|x â’ 3| 4 f(x) = â’|x 3| 4 f(x) = â’|x â’ 4| 3 f(x) = â’|x 4| 3.

Answer 1

Functions are used to represent graphs, and vice versa.

The function represented by the graph is $f(x) =- |x + 4| + 3$

The graph (see attachment) is an absolute value graph.

An absolute value graph is represented as:

$f(x) =a |x - h| + k$

Where

$Vertex = (h,k)$

The vertex is the minimum or the maximum point on the graph.

So, we have:

$Vertex = (-4,3)$

The function becomes

$f(x) =a |x + 4| + 3$

The function also passes through the point (-1,0).

So, we have:

$0 =a |-1 + 4| + 3$

$0 =a |3| + 3$

Remove the absolute bracket

$0 =3a + 3$

Subtract 3 from both sides

$3a =- 3$

Divide both sides by 3

$a =- 1$

Substitute -1 for (a) in $f(x) =a |x + 4| + 3$

$f(x) =- |x + 4| + 3$

Hence, the function represented by the graph is $f(x) =- |x + 4| + 3$

Read more about absolute value graphs at:

brainly.com/question/3381225