Question

NO LINKS!!! Please help me with this graph. Part 6a​

Answer 1

Answer:

$\large{\boxed{ \ g(x) = -\dfrac{7}{4} | x -5| +0 \ }}$

Explanation:

Absolute value of a graph formula:

• y = a |x -h| + k

Identify the vertex : (h, k) = (5, 0)

Take two points : (5, 0), (9, -7)

$\sf Find \ slope \ (a) : \sf \ \dfrac{y_2 - y_1}{x_2- x_1} \ = \ \dfrac{-7-0}{9-5} \ = \ -\dfrac{7}{4}$

Join the variables together:   $\bf g(x) = - \dfrac{7}{4} | x -5| +0$

Answer 2

Answer:

$f(x) = -\dfrac{7}{4}|x-5|+0$

Step-by-step explanation:

The function in the coordinate Plane is an absolute value function . Consider the parent function

$f(x) = |x|$

Recall the properties of transformation

• f(x+a), If a<0 ⇒ It moves to right
• a.f(x),If a<0 ⇒ It flips upsidedown
• f(x)+a,If a>0 ⇒ It moves up & a<0 It moves down

From the inspection of the graph,It has moved to right by 5 units, Thus

$f(x - 5) = |x - 5|$

Apparently, It has neither shifted up or down, hence

$f(x - 5) +0= |x - 5|+0$

Looking at the graph, we can see that it has been reflected vertically. It tells us we have to multiply it by a negative constant

$-a f(x - 5) +0= -a |x - 5| +0$

take (9,7) to figure out a.

• set x to 9 and the LHS expression to 7

$-a | 9- 5| =7$

Solving the equation yields:

$\boxed{a = - \frac{7}{4} }$

hence, our function is $\boxed{f(x) = -\dfrac{7}{4}|x-5|+0}$