Question

NO LINKS!! Please help me with this graph. Part 2​

Answer 1

`g(x)=(2)/(3)|x-6|-7`

Step-by-step explanation:

Translations

For
`a > 0`

`f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}`

`f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}`

`y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis by a factor of}\:a`

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Parent function:
`f(x)=|x|`

`f(0)=|0|=0 \implies \textsf{The vertex of the parent function is at (0, 0)}`

From inspection of the graph, the vertex of the transformed function is at (6, -7). Therefore, there has been a translation of:

• 6 units right
• 7 units down

`\textsf{6 units right}\implies f(x-6) =|x-6|`

`\textsf{and 7 units down}\implies f(x-6)-7=|x-6|-7`

From inspection of the graph, we can see that it has been stretched parallel to the y-axis:

`\implies a\:f(x-6)-7=a|x-6|-7`

The line goes through point (0, -3)

Substituting this point into the above equation to find
`a`:

`\implies a|0-6|-7=-3`

`\implies 6a=4`

`\implies a=(2)/(3)`

Therefore,

`\implies g(x)=(2)/(3)|x-6|-7`

Answer 2

`\large{\boxed x -6}`

Step-by-step explanation:

Absolute value of a graph formula:

• y = a |x -h| + k

Identify the vertex : (h, k) = (6, -7)

Take two points: (6, -7), (9, -5)

`\sf Find \ slope \ (a) : \sf \ (y_2 - y_1)/(x_2- x_1) \ = \ \ (-5-(-7))/(9-6) \ = \ \ (2)/(3)`

Join them to build the equation:
`\bfx - 6`