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Let f(x) = 2√x. If g(x) is the graph of f(x) shifted up 3 units and left 2 units, write a formula for g(x). g(x) = Enter √ as sqrt(x). x Question Help: Video

Let f(x) = 2√x. If g(x) is the graph of f(x) shifted up 3 units and left 2 units, write a formula for g(x). g(x) = Enter √ as sqrt(x). x Question Help: Video

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter6: Exponential And Logarithmic Functions
Section6.2: Graphs Of Exponential Functions
Problem 2SE: What is the advantage of knowing how to recognizetransformations of the graph of a parent...
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**Title: Graph Transformations in Algebra** **Section: Understanding Function Transformations** ---- **Example Problem on Graph Transformations** **Original Function:** Let \( f(x) = 2\sqrt{x} \). **Transformation Instructions:** If \( g(x) \) is the graph of \( f(x) \) shifted up 3 units and left 2 units, write a formula for \( g(x) \). **Solution:** To find \( g(x) \), apply the given transformations to the original function \( f(x) \). **Step-by-step Instructions:** 1. **Horizontal Shift (Left 2 units):** - This means we replace \( x \) with \( (x + 2) \) in the original function. - So, \( f(x) = 2\sqrt{x} \) becomes \( f(x + 2) = 2\sqrt{x + 2} \). 2. **Vertical Shift (Up 3 units):** - This means we add 3 to the function after the horizontal shift. - So, \( f(x + 2) \) becomes \( 2\sqrt{x + 2} + 3 \). Thus, the formula for \( g(x) \) is: \[ g(x) = 2\sqrt{x + 2} + 3 \] **Input Notation:** - Enter \( \sqrt{x} \) as sqrt(x). **Interactive Help:** - For additional guidance, you can watch an instructional video by clicking on the "Video" link provided. **Visual Representation:** - There are no graphical elements in this example, but typically, shifts in the graph would be represented by plotting the original function and then showing the shifted function to verify the transformation. --- **Note:** Analyzing graph transformations helps in understanding how the function's graph changes with various operations applied to the function's equation.
Transcribed Image Text:**Title: Graph Transformations in Algebra** **Section: Understanding Function Transformations** ---- **Example Problem on Graph Transformations** **Original Function:** Let \( f(x) = 2\sqrt{x} \). **Transformation Instructions:** If \( g(x) \) is the graph of \( f(x) \) shifted up 3 units and left 2 units, write a formula for \( g(x) \). **Solution:** To find \( g(x) \), apply the given transformations to the original function \( f(x) \). **Step-by-step Instructions:** 1. **Horizontal Shift (Left 2 units):** - This means we replace \( x \) with \( (x + 2) \) in the original function. - So, \( f(x) = 2\sqrt{x} \) becomes \( f(x + 2) = 2\sqrt{x + 2} \). 2. **Vertical Shift (Up 3 units):** - This means we add 3 to the function after the horizontal shift. - So, \( f(x + 2) \) becomes \( 2\sqrt{x + 2} + 3 \). Thus, the formula for \( g(x) \) is: \[ g(x) = 2\sqrt{x + 2} + 3 \] **Input Notation:** - Enter \( \sqrt{x} \) as sqrt(x). **Interactive Help:** - For additional guidance, you can watch an instructional video by clicking on the "Video" link provided. **Visual Representation:** - There are no graphical elements in this example, but typically, shifts in the graph would be represented by plotting the original function and then showing the shifted function to verify the transformation. --- **Note:** Analyzing graph transformations helps in understanding how the function's graph changes with various operations applied to the function's equation.
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