Question

In Exercises $25-28$ , the graph is that of a function $y=f(x)$ that can be obtained by transforming the graph of $y=\sqrt{x} .$ Write a formula for the function $f$

Name: Problem 27, Chapter 1: Precalculus: Graphical, Numerical, Algebraic
Uploaded: 2023-09-14T23:14:18-08:00
Duration: 3 min 12 s
Channel: Alexander Frasco
Description: In Exercises 25-28 , the graph is that of a function y=f(x) that can be obtained by transforming the graph of y=√(x) . Write a formula for the function f

   In Exercises $25-28$ , the graph is that of a function $y=f(x)$ that can be obtained by transforming the graph of $y=\sqrt{x} .$ Write a formula for the function $f$

Precalculus: Graphical, Numerical, Algebraic

Franklin D.… 8th Edition

Chapter 1, Problem 27

Instant Answer

Solved by Expert Alexander Frasco

09/14/2023

Step 1

We are given that the graph of the function is moved two units to the left. This transformation can be represented by replacing $x$ with $x+2$ in the original function. So, the function becomes $y=\sqrt{x+2}$. Show more…

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In Exercises $25-28$ , the graph is that of a function $y=f(x)$ that can be obtained by transforming the graph of $y=\sqrt{x} .$ Write a formula for the function $f$

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Key Concepts

Function Transformations

This concept involves modifying the graph of a base function by applying operations such as translations (shifting the graph horizontally or vertically), stretches or compressions (altering the scale of the graph along the x? or y–axis), and reflections (flipping the graph across a line). These operations allow you to create new functions from a known function while maintaining its essential structure.

Square Root Function

The square root function, typically represented as y = sqrt(x), is a basic function that produces a characteristic curve starting at the origin and increasing gradually. It serves as an important base function for learning about transformations, as its graph is often manipulated to explore the effects of various shifts, stretches, and reflections.

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