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The graph of g(x) is f(x) after it has been stretched vertically by a factor of 3, translated to the left 2 units, and up 8 units. What is the function rule for g(x) given f(x)=x2
To find the function rule for g(x), we need to apply the given transformations to f(x) = x^2.
1. Stretch vertically by a factor of 3:
To stretch the graph vertically by a factor of 3, we multiply the function by 3. Therefore, the new function after the vertical stretch is 3*f(x) = 3*x^2.
2. Translate to the left 2 units:
To translate the graph to the left 2 units, we substitute x+2 in place of x in the function. Therefore, the new function after the translation to the left is 3*f(x+2) = 3*(x+2)^2.
3. Move up 8 units:
To move the graph up 8 units, we add 8 to the function. Therefore, the final function rule for g(x) is g(x) = 3*(x+2)^2 + 8.
To find the function rule for g(x), we need to apply the given transformations to f(x)=x^2.
1. Stretching vertically by a factor of 3: Multiply the entire function by 3.
g1(x) = 3 * f(x)
= 3 * x^2
2. Translating to the left 2 units: Subtract 2 from x.
g2(x) = g1(x-2)
= 3 * (x-2)^2
3. Moving up 8 units: Add 8 to the entire function.
g(x) = g2(x) + 8
= 3 * (x-2)^2 + 8
Therefore, the function rule for g(x) is g(x) = 3 * (x-2)^2 + 8.