Math

Question Translate the graph of y=xy=|x| to the graph of y=x+5+3y=|x+5|+3.

Studdy Solution

STEP 1

Assumptions1. The original graph is y=xy=|x| . The target graph is y=x+5+3y=|x+5|+3
3. The graph of y=xy=|x| is a V-shaped graph with the vertex at the origin (0,0), opening upwards.
4. The graph of y=x+5+3y=|x+5|+3 is a translation of the original graph.

STEP 2

First, we need to understand what the graph of y=x+5+y=|x+5|+ represents. The graph of y=x+5+y=|x+5|+ is a translation of the graph of y=xy=|x|.

STEP 3

We can break down the translation into two parts horizontal and vertical. The horizontal translation is represented by the "+5" inside the absolute value function, and the vertical translation is represented by the "+3" outside the absolute value function.

STEP 4

For the horizontal translation, the "+" inside the absolute value function means we shift the graph to the left by units. This is because the "+" is subtracted from x, moving the graph to the left.

STEP 5

For the vertical translation, the "+3" outside the absolute value function means we shift the graph upwards by3 units. This is because the "+3" is added to the y-value, moving the graph upwards.

STEP 6

So, to translate the graph of y=xy=|x| to make it the graph of y=x+5+3y=|x+5|+3, we need to shift the graph to the left by5 units and upwards by3 units.

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