Question

hw 3.6 category: homework current learning objective: graphing an absolute value function question 11 practice similar questions score: 0 of 1 point write an absolute - value function that has been reflected across the x - axis, shrunk by 5/7, translated right by 3, and translated down by 2. f(x)= enter your answer submit answer attempts: 0/3 find this question difficult? do you know you can practice another version of this question? need help? dont know how to get started? stuck on a specific step? rest assured, mathgpt is here to help whenever you need it ask mathgpt unlimited ai tutoring

Explanation:

Step1: Start with basic absolute - value function

The basic absolute - value function is $y = |x|$.

Step2: Reflect across the x - axis

When a function $y = f(x)$ is reflected across the $x$ - axis, the transformation is $y=-f(x)$. So, for $y = |x|$, it becomes $y = -|x|$.

Step3: Shrink vertically

To shrink a function $y = f(x)$ vertically by a factor $a$, the transformation is $y = a\cdot f(x)$. Here, $a=\frac{5}{7}$, so the function becomes $y=-\frac{5}{7}|x|$.

Step4: Translate right by 3

To translate a function $y = f(x)$ to the right by $h$ units, the transformation is $y = f(x - h)$. Here, $h = 3$, so the function becomes $y=-\frac{5}{7}|x - 3|$.

Step5: Translate down by 2

To translate a function $y = f(x)$ down by $k$ units, the transformation is $y=f(x)-k$. Here, $k = 2$, so the final function is $f(x)=-\frac{5}{7}|x - 3|-2$.

Answer:

$f(x)=-\frac{5}{7}|x - 3|-2$