The graph of g(x) is wider than f(x) and is shifted to the left 2 units and down 1 unit , Option C is the correct answer.
<h3>What is a function ?</h3>
A function is a mathematical statement which relates , a dependent variable and an independent variable.
The transformation being described is from
f(x)=x² to g(x)=3(x+2)²-1
f(x)=x2→g(x)=3(x−2)2+1
The horizontal shift depends on the value of h
The horizontal shift is described as:
g(x) = f(x+h) The graph is shifted to the left h units.
g(x) = f(x-h) The graph is shifted to the right h units
Horizontal Shift: Left 2 Units
The vertical shift depends on the value of k
. The vertical shift is described as:
g(x) = f(x) +k The graph is shifted up k units
g(x) = f(x) -k The graph is shifted down k units.
Vertical Shift: Down 1 Units
Compressing and stretching depends on the value of a
When a is greater than 1: Vertically stretched
When a is between 0 and 1: Vertically compressed
Vertical Compression or Stretch: Stretched
Therefore seeing to the option, Option C is the correct answer
The graph of g(x) is wider than f(x) and is shifted to the left 2 units and down 1 unit.
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