the graph of f(x) = |x| is translated 6 units to the right and 2 units up to form a new function. which…

the graph of f(x) = |x| is translated 6 units to the right and 2 units up to form a new function. which statement about the range of both functions is true?\no the range is the same for both functions: {y | y is a real number}.\no the range is the same for both functions: {y | y ≥ 0}.\no the range changes from {y | y ≥ 0} to {y | y ≥ 2}.\no the range changes from {y | y ≥ 0} to {y | y ≥ 6}.

the graph of f(x) = |x| is translated 6 units to the right and 2 units up to form a new function. which statement about the range of both functions is true?\no the range is the same for both functions: {y | y is a real number}.\no the range is the same for both functions: {y | y ≥ 0}.\no the range changes from {y | y ≥ 0} to {y | y ≥ 2}.\no the range changes from {y | y ≥ 0} to {y | y ≥ 6}.

Answer

Explanation:

Step1: Recall the range of original function

The function $f(x)=|x|$ has a range of ${y|y\geq0}$ since the absolute - value of any real number is non - negative.

Step2: Analyze the translation

When the graph of $y = f(x)$ is translated 6 units to the right and 2 units up, the new function is $g(x)=|x - 6|+2$. For any real number $x$, $|x - 6|\geq0$, so $g(x)=|x - 6|+2\geq2$. The range of $g(x)$ is ${y|y\geq2}$.

Answer:

The range changes from ${y|y\geq0}$ to ${y|y\geq2}$.