The function Y2 is defined as Y1+k for some real number k. Based on the two views of the graphs

step 1 So now we have according to the graph y2 is equal to y1 plus k so therefore now we will substitu

The function Y2 is defined as Y1+k for some real number k....

The function $\mathrm{Y}_{2}$ is defined as $\mathrm{Y}_{1}+k$ for some real number $k$. Based on the two views of the graphs of $\mathrm{Y}_{1}$ and $\mathrm{Y}_{2}$ and the displays at the bottoms of the screens, what is the value of $k ?$ $(-4,3)$ lies on the graph of $Y_{1}$ First view (Graph can't copy) $(-4,8)$ lies on the graph of $Y_{2}$ Second view (Graph can't copy)

The function $\mathrm{Y}_{2}$ is defined as $\mathrm{Y}_{1}+k$ for some real number $k$. Based on the two views of the graphs of $\mathrm{Y}_{1}$ and $\mathrm{Y}_{2}$ and the displays at the bottoms of the screens, what is the value of $k ?$
$(-4,3)$ lies on the graph of $Y_{1}$ First view
(Graph can't copy)
$(-4,8)$ lies on the graph of $Y_{2}$ Second view
(Graph can't copy)

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Key Concepts

Vertical Translation

Vertical translation is a type of function transformation where a constant is added to the output of a function, resulting in a shift of the graph up or down. If a function Y2 is defined as Y1 + k, the entire graph of Y1 is moved vertically by k units. Positive values of k shift the graph upward, while negative values shift it downward.

Coordinate Mapping

Coordinate mapping involves understanding how points on the graph of one function correspond to points on the transformed function. In the context given, if a point (x, y) lies on the original function Y1, then the corresponding point on Y2 will be (x, y + k). This relationship is crucial for determining the value of k when specific points on each graph are known.

Function Transformation

Function transformation refers to the process of modifying a function's formula to create a new function with a shifted, stretched, or otherwise altered graph. In the case of adding a constant k to a function, the transformation is a simple vertical shift, which can be easily identified by analyzing corresponding points on the original and transformed graphs.

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