The graph of y=|x| is shifted down by 9 units and to the right by 4 units. What is the equation of the new graph? Choose 1 answer: (A) y=|x-4|-9 (B) y=|x-9|+4 (C) y=|x-9|-4 (D) y=|x-4|+9

Understanding shifts in equations: To determine the equation of the transformed graph, we need to understand how shifts affect the equation of a function. A shift to the right by 'h' units will replace 'x' with 'x-h' in the function's equation. A shift down by 'k' units will subtract 'k' from the function's value.Shifting the graph to the right: Since the original function is y = |x|, shifting the graph to the right by 4 units will replace 'x' with 'x-4'. This gives us the intermediate function y = |x-4|.Shifting the graph down: Next, shifting the graph down by 9 units will subtract 9 from the value of the function. This modifies our intermediate function to y = |x-4| - 9.Comparing and choosing the correct equation: Now we compare our result with the given choices to find the correct equation. The equation y = |x-4| - 9 matches choice (A).

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The graph of
y=|x| is shifted down by 9 units and to the right by 4 units.
What is the equation of the new graph?
Choose 1 answer:
(A)
y=|x-4|-9
(B)
y=|x-9|+4
(C)
y=|x-9|-4
(D)
y=|x-4|+9

The graph of $y=|x|$ is shifted down by $9$ units and to the right by $4$ units. $\newline$ What is the equation of the new graph? $\newline$ Choose $1$ answer: $\newline$ (A) $y=|x-4|-9$ $\newline$ (B) $y=|x-9|+4$ $\newline$ (C) $y=|x-9|-4$ $\newline$ (D) $y=|x-4|+9$

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Algebra 2

Domain and range of absolute value functions: equations

Full solution

Q. The graph of

y=|x|

is shifted down by

9

units and to the right by

4

units.

\newline

What is the equation of the new graph?

\newline

Choose

1

answer:

\newline

(A)

y=|x-4|-9

\newline

(B)

y=|x-9|+4

\newline

(C)

y=|x-9|-4

\newline

(D)

y=|x-4|+9

Understanding shifts in equations: To determine the equation of the transformed graph, we need to understand how shifts affect the equation of a function. A shift to the right by $h$ units will replace $x$ with $x-h$ in the function's equation. A shift down by $k$ units will subtract $k$ from the function's value.
Shifting the graph to the right: Since the original function is $y = |x|$ , shifting the graph to the right by $4$ units will replace ' $x$ ' with ' $x-4$ '. This gives us the intermediate function $y = |x-4|$ .
Shifting the graph down: Next, shifting the graph down by $9$ units will subtract $9$ from the value of the function. This modifies our intermediate function to $y = |x-4| - 9$ .
Comparing and choosing the correct equation: Now we compare our result with the given choices to find the correct equation. The equation $y = |x-4| - 9$ matches choice (A).