Question

NO LINKS!!!! Please help me with this graph. Part 7a​

Answer 1

Answer:

$\large \boxed{ \sf y=-0.3\left|x-0\right|-7}$

Explanation:

Absolute value of a graph formula:

• y = a |x -h| + k

Identify the vertex : (h, k) = (0, -7)

As the graph opens downward, take negative/fall coordinates.

Two points: (0, -7), (10, -10)

$\sf Find \ slope \ (a) : \sf \ \dfrac{y_2 - y_1}{x_2- x_1} \ = \ \dfrac{-10-(-7)}{10-0} \ = -0.3$

Put them together: $\bf y = -0.3|x - 0| -7 \ \ \ \approx \ \ y = -0.3|x| - 7$

Answer 2

Answer:

$g(x)=-\dfrac{3}{10}|x|-7$

Step-by-step explanation:

Translations

For $a > 0$

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

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

$y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}$

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

Parent function:  $f(x)=|x|$

From inspection of the graph, the transformed function has been reflected in the x-axis.

$\implies -f(x)=-|x|$

The vertex of the parent function is the origin (0, 0).  The vertex of the transformed function is at (0, -7).  Therefore, there has been a translation of 7 units down.

$\implies -f(x)-7=-|x|-7$

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

$\implies -a\:f(x)-7=-a|x|-7$

The line goes through point (10, -10)

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

$\implies -a|10|-7=-10$

$\implies -10a=-3$

$\implies a=\dfrac{3}{10}$

Therefore,

$\implies g(x)=-\dfrac{3}{10}|x|-7$