Question

The function $Y_{2}$ is defined as $Y_{1}+k$ for some real number $k$. Based on the two views of the graphs of $Y_{1}$ and $Y_{2}$ and the displays at the bottoms of the screens, what is the value of $k ?$ (Graph cannot copy)

Name: Problem 29, Chapter 2: A Graphical Approach to Precalculus with Limits
Uploaded: 2020-08-17T00:14:27-08:00
Duration: 2 min 20 s
Channel: Nick Johnson
Description: The function Y2 is defined as Y1+k for some real number k. Based on the two views of the graphs of Y1 and Y2 and the displays at the bottoms of the screens, what is the value of k ? (Graph cannot copy)

   The function $Y_{2}$ is defined as $Y_{1}+k$ for some real number $k$. Based on the two views of the graphs of $Y_{1}$ and $Y_{2}$ and the displays at the bottoms of the screens, what is the value of $k ?$
(Graph cannot copy)

A Graphical Approach to Precalculus with Limits

John Hornsby,… 7th Edition

Chapter 2, Problem 29

Instant Answer

Solved by Expert Nick Johnson

08/17/2020

Step 1

Step 1: From the given information, we know that the function $Y_{1}$ is defined as $\sqrt{x-2}$ and the function $Y_{2}$ is defined as $\sqrt{x-2}+k$. Show more…

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The function $Y_{2}$ is defined as $Y_{1}+k$ for some real number $k$. Based on the two views of the graphs of $Y_{1}$ and $Y_{2}$ and the displays at the bottoms of the screens, what is the value of $k ?$ (Graph cannot copy)

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Key Concepts

Graphical Comparison

Analyzing the differences between two function graphs can reveal the nature of their transformation. By comparing key features such as intercepts, one can deduce the magnitude and direction of the shift introduced between the original and transformed functions.

Function Transformation

This concept involves altering the function's equation to produce a modified function. In particular, adding a constant is a transformation that shifts all y-values uniformly, illustrating how algebraic changes affect the graphical representation of functions.

Vertical Shift

Adding a constant to a function's output results in a vertical shift of its graph. The entire graph moves upward if the constant is positive and downward if it is negative, without altering the shape or features of the original function.

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