the graph of $f(x) = |x|$ is reflected across the y-axis and translated to the left 5 units. which statement…

the graph of $f(x) = |x|$ is reflected across the y-axis and translated to the left 5 units. which statement about the domain and range of each function is correct?○ both the domain and range of the transformed function are the same as those of the parent function.○ neither the domain nor the range of the transformed function are the same as those of the parent function.○ the range of the transformed function is the same as the parent function, but the domains of the functions are different.○ the domain of the transformed function is the same as the parent function, but the ranges of the functions are different.

the graph of $f(x) = |x|$ is reflected across the y-axis and translated to the left 5 units. which statement about the domain and range of each function is correct?○ both the domain and range of the transformed function are the same as those of the parent function.○ neither the domain nor the range of the transformed function are the same as those of the parent function.○ the range of the transformed function is the same as the parent function, but the domains of the functions are different.○ the domain of the transformed function is the same as the parent function, but the ranges of the functions are different.

Answer

Explanation:

Step1: Find parent function domain/range

Parent function: $f(x)=|x|$ Domain: All real numbers, $(-\infty, \infty)$ Range: All non-negative real numbers, $[0, \infty)$

Step2: Apply transformations to function

Reflect across y-axis: $f(-x)=|-x|=|x|$ Translate left 5 units: $g(x)=|x+5|$

Step3: Find transformed function domain/range

Transformed function: $g(x)=|x+5|$ Domain: All real numbers, $(-\infty, \infty)$ Range: All non-negative real numbers, $[0, \infty)$

Step4: Compare domain/range of both functions

Domain of $f(x)$ and $g(x)$ are identical; range of $f(x)$ and $g(x)$ are identical.

Answer:

Both the domain and range of the transformed function are the same as those of the parent function.