Question

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

Answer 1

Answer:

$\large{\boxed{\sf y = \dfrac{2}{3} | x -6|- 7}}$

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)

 $\sf Find \ slope \ (a) : \sf \ \dfrac{y_2 - y_1}{x_2- x_1} \ = \ \ \dfrac{-5-(-7)}{9-6} \ = \ \ \dfrac{2}{3}$

Join them to build the equation:   $\bf{y = \dfrac{2}{3} |x - 6| - 7}$

Answer 2

Answer:

$g(x)=\dfrac{2}{3}|x-6|-7$

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 $a$:

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

$\implies 6a=4$

$\implies a=\dfrac{2}{3}$

Therefore,

$\implies g(x)=\dfrac{2}{3}|x-6|-7$