Question

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

Answer 1

Answer:

$\large{\boxed{\sf g(x) = \dfrac{1}{2} |x - 4| +7}}$

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)

$\sf Find \ slope \ (a) : \sf \ \dfrac{y_2 - y_1}{x_2- x_1} \ = \ \dfrac{8-7}{6-4} \ = \dfrac{1}{2}$

Putting them together :  $\bf g(x) = \dfrac{1}{2} |x - 4| +7$

Answer 2

Answer:

$g(x)=\dfrac{1}{2}|x-4|+7$

Step-by-step explanation:

Translations

For $a > 0$

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

$f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}$

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

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

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 $a$:

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

$\implies 4a=2$

$\implies a= \dfrac{1}{2}$

Therefore,

$\implies g(x)=\dfrac{1}{2}|x-4|+7$