The graph of the parent function y = x is horizontally stretched by a factor of 5 and reflected over the y-axis. What is the
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Using translation concepts, the graph of f(x) = (x - 2)² + 3 is given at the end of the question.
<h3>What is a translation?</h3>A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
In this problem, we have that the parent and the translated function are given, respectively, by:
- g(x) = x².
- f(x) = (x - 2)² + 3.
The translations are as follows:
- Right two units, as x -> x - 2.
- Up 3 units, because f(x) = g(x) + 3.
Hence the graphs are given at the end of the answer, with the parent function in red and the translated function f(x) = (x - 2)² + 3 in green.
More can be learned about translation concepts at brainly.com/question/4521517
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a. (f+g)(x) = 8x+2
b. (f-g)(x) = 4x-6
Step-by-step explanation:
Given
<u>a. (f+g)(x)</u>
<u>b. (f-g)(x)</u>
Hence,
a. (f+g)(x) = 8x+2
b. (f-g)(x) = 4x-6
Keywords: Functions
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