Sketch a graph of -f(x + 1)

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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11) Graphed below is the function g(x) and a transformation of g(x). Write an equation
for the transformation.
12) Shown below is a graph of f(x). Sketch a graph of -f(x + 1)
Transcribed Image Text:11) Graphed below is the function g(x) and a transformation of g(x). Write an equation for the transformation. 12) Shown below is a graph of f(x). Sketch a graph of -f(x + 1)
Expert Solution
Question 11

Let's say graph (2) is represented by function f(x) as graph (1) is represented by g(x).

If we observe the graphs of the first question, then we will observe

  • If we create a mirror image of the graph (1) representing g(x) then we get a graph to let's say graph (1') representing

           g(-x).

  • Graph (1') has a similar shape to graph (2) but a different size. That means graph (2) is the mirror image of the graph (1) representing g(x) about the y-axis.
  • Now if we see the plot the graph (1') and graph (2) in the same plane we will observe that for every x the value of 

         f(x) = 2*g(-x).

The graph of g(1') and g(2) representing g(-x) and f(x)

Algebra homework question answer, step 1, image 1

So, the equation of graph (2) with respect to g(x) is, 2g(-x).

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