he 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 stretch the graph of f(x) vertically by a factor of 3, multiply f(x) by 3.
To translate the graph of f(x) to the left 2 units, subtract 2 from x.
To translate the graph of f(x) up 8 units, add 8.
Therefore, the function rule for g(x) is:
g(x) = 3(x+2)^2 + 8
To find the function rule for g(x), we can apply the transformations to f(x)=x^2 step by step:
1. Stretch vertically by a factor of 3: Multiply f(x) by 3.
g(x) = 3 * f(x) = 3 * x^2
2. Translate to the left 2 units: Replace x with (x + 2).
g(x) = 3 * (x + 2)^2
3. Translate up 8 units: Add 8 to the expression.
g(x) = 3 * (x + 2)^2 + 8
Therefore, the function rule for g(x) is g(x) = 3 * (x + 2)^2 + 8.