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

NO LINKS!! Please help me with this graph. Part 2​-example-1

2 Answers

8 votes

Answer:


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

-----------------------------------------------------------------------------------------

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

User Wapac
by
8.6k points
9 votes

Answer:


\large{\boxed- 7}

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

User Sjstrutt
by
8.1k points

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