Answer :
[tex]\boxed{k=4}[/tex]
Explanation:
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Let's rewrite the question for better understand:
Given f(x) and g(x) = f(x + k), use the graph to determine the value of k. Two lines labeled f(x) and g(x). Line f(x) passes through points and (2, 2). Line g(x) passes through points (-4, 0) and (-1,3).
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From the question, we know that the graph of g(x) has the same form of f(x) but it's been shifted k units either to the left or to the right, so:
- If k > 0 the graph has been shifted k units to the left
- If k < 0 the graph has been shifted k units to the right
From g(x) we know:
[tex]It \ passes \ through \ (-4, 0) \ (-1,3). \\ \\ \\ Point-slope \ form \ of \ the \ equation \ of \ a \ line: \\ \\ y-0=\frac{3-0}{-1-(-4)}(x-(-4)) \\ \\ y=x+4 \\ \\ \\ So: \\ \\ g(x)=x+4[/tex]
f(x) must have the same slope as g(x), so:
[tex]f(x)=x+b \\ \\ \\ (2,2) \ is \ a \ point \ on \ the \ line, \ so \ the \ y-intercept: \\ \\ 2=2+b \\ \\ b=0 \\ \\ \\ Finally: \\ \\ f(x)=x[/tex]
By comparing f(x) and g(x), we know that:
[tex]f(x)=x \\ \\ g(x)=x+4 \\ \\ \\ Then: \\ \\ \boxed{k=4}[/tex]
Learn more:
Proportional relationships: https://brainly.com/question/674693
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