Question

Use the given parent function f(x)=|x| to graph g(x)=|x+2|-4. use the ray tool and select two points to graph each ray. ​

I answer my own question.

Answer 1

Shown in the attached figure

Explanation:

The absolute value function is a function that takes the shape of a V. The pattern of the absolute value function is:

$f(x)=\mid x \mid$

So we need to use this function in order to obtain:

$g(x)=\mid x+2 \mid -4$

Recall that to translate a function vertically, we use the following rule:

$g(x)=f(x)+k \\ \\ \bullet \ If \ k>0 \ the \ graph \ of \ f(x) \ is \ translated \ k \ units \ up \\ \\ \bullet \ If \ k<0 \ the \ graph \ of \ f(x) \ is \ translated \ k \ units \ down$

And to translate a function horizontally, we use the following rule:

$g(x)=f(x+c) \\ \\ \bullet \ If \ c>0 \ the \ graph \ of \ f(x) \ is \ translated \ c \ units \ to \ the \ left \\ \\ \bullet \ If \ c<0 \ the \ graph \ of \ f(x) \ is \ translated \ c \ units \ to \ the \ right$

Since:

$c=2>0 \  and \ k=-4<0$

Then:

g(x) is the translation of f(x) 2 units to the left and 4 units down

Learn more:

Transformations in real-world problems: https://brainly.com/question/1033817

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