document.write( "Question 1199724: Given f(x) = 3x + 1, and g(x) = -2 • f(x) - 1. Describe the transformations(list them) and write the new simplified equation for g(x). \n" ); document.write( "
Algebra.Com's Answer #848163 by textot(100)\"\" \"About 
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**1. Transformations:**\r
\n" ); document.write( "\n" ); document.write( "* **Vertical Stretch:** The coefficient -2 stretches the graph of f(x) vertically by a factor of 2.
\n" ); document.write( "* **Reflection in the x-axis:** The negative sign in front of -2f(x) reflects the graph of f(x) across the x-axis.
\n" ); document.write( "* **Vertical Shift:** The \"-1\" at the end of the equation shifts the graph of -2f(x) downward by 1 unit.\r
\n" ); document.write( "\n" ); document.write( "**2. Simplified Equation for g(x)**\r
\n" ); document.write( "\n" ); document.write( "* g(x) = -2 * f(x) - 1
\n" ); document.write( "* g(x) = -2 * (3x + 1) - 1
\n" ); document.write( "* g(x) = -6x - 2 - 1
\n" ); document.write( "* g(x) = -6x - 3\r
\n" ); document.write( "\n" ); document.write( "**Therefore:**\r
\n" ); document.write( "\n" ); document.write( "* The transformations applied to f(x) to obtain g(x) are: vertical stretch by a factor of 2, reflection in the x-axis, and a vertical shift downward by 1 unit.
\n" ); document.write( "* The simplified equation for g(x) is g(x) = -6x - 3.
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