Question

NO LINKS!!! Please help me with this graph. Part 4a​

Answer 1

`g(x)=(1)/(2)|x-4|+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 up}`

`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|`

(with vertex at the origin)

From inspection of the graph, the vertex of the transformed function is at (4, 7). Therefore, there has been a translation of:

• 4 units right
• 7 units up

`\implies f(x-4)+7=|x-4|+7`

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

`\implies a\:f(x-4)+7=a|x-4|+7`

The line goes through point (0, 9)

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

`\implies a|0-4|+7=9`

`\implies 4a=2`

`\implies a= (1)/(2)`

Therefore,

`\implies g(x)=(1)/(2)|x-4|+7`

Answer 2

`\large{\boxed +7}`

Step-by-step explanation:

Absolute value of a graph formula:

• y = a |x -h| + k

Identify the vertex : (h, k) = (4, 7)

Take two points: (4, 7), (6, 8)

`\sf Find \ slope \ (a) : \sf \ (y_2 - y_1)/(x_2- x_1) \ = \ (8-7)/(6-4) \ = (1)/(2)`

Putting them together :
`\bf g(x) = (1)/(2) |x - 4| +7`