QuestionDetermine the final function after shifting $y=|x|$ up 7 units, reflecting it over the $x-$ axis, and shifting right 9 units.

Studdy Solution

STEP 1

Assumptions1. The original function is $y=|x|$ . The transformations are applied in the following order shift up7 units, reflect about the $x-$ axis, and shift right9 units

STEP 2

First, we will shift the graph of the function up by7 units. This can be done by adding7 to the function.
$y = |x| +7$

STEP 3

Next, we reflect the graph about the $x-$ axis. This can be done by multiplying the function by -1.
$y = -(|x| +7)$

STEP 4

Finally, we shift the graph to the right by9 units. This can be done by replacing $x$ with $(x-9)$ in the function.
$y = -|x-9| -7$ The function that is finally graphed after the transformations is $y = -|x-9| -7$ .

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