Transform the function f(x)=|x|

Question

--translate right 1 unit and translate up 5 units. The resulting function as an equation is:(1 point)
Responses

y=|x−1|−5
y is equal to start absolute value x minus 1 end absolute value minus 5

y=|x+1|+5
y is equal to start absolute value x plus 1 end absolute value plus 5

y=|x−1|+5
y is equal to start absolute value x minus 1 end absolute value plus 5

y=|x+1|−5

Answer 1

To transform the function \( f(x) = |x| \) by translating it right 1 unit and up 5 units, we apply the following transformations:

1. Translate right 1 unit: This replaces \( x \) with \( x - 1 \), resulting in the function \( f(x) = |x - 1| \).

2. Translate up 5 units: This adds 5 to the entire function, resulting in \( f(x) = |x - 1| + 5 \).

So, the resulting equation after both transformations is:

\[ y = |x - 1| + 5 \]

Thus, the correct response is:

y = |x−1| + 5