Question

8 multiple choice 1 point consider the graph of y = |x|. it is flipped over the x - axis and translated (or slid) 2 units to the right. what is the equation of the resulting graph? y = |x| - 2 y = -|x - 2| y = |-x - 2| y = -|x + 2| 9 essay 1 point consider y = |2x - 10|. a) does this have a maximum or a minimum? b) what is this maximum or minimum value? c) what is the value of x at this maximum or minimum value?

Explanation:

Step1: Analyze reflection over x - axis

When a graph of $y = f(x)$ is flipped over the $x$-axis, the transformation is $y=-f(x)$. For $y = |x|$, it becomes $y=-|x|$.

Step2: Analyze translation 2 units to the right

When a graph of $y = f(x)$ is translated $h$ units to the right, the transformation is $y = f(x - h)$. Here $h = 2$, so for $y=-|x|$, the new equation is $y=-|x - 2|$.

for question 9:

Step1: Recall properties of absolute - value functions

The absolute - value function $y = |a|$ is always non - negative, i.e., $y=|a|\geq0$ for all real values of $a$. For the function $y = |2x - 10|$, since the absolute value of any real number is non - negative, it has a minimum.

Step2: Find the minimum value

The minimum value of an absolute - value function $y = |a|$ is 0. So, the minimum value of $y = |2x - 10|$ is 0.

Step3: Find the x - value at the minimum

Set the expression inside the absolute - value equal to 0. So, $2x-10 = 0$. Solving for $x$:
$2x=10$, then $x = 5$.

Answer:

B. $y=-|x - 2|$