Question
What transformations of f(x) = x2 are applied to the function g(x) = 2(x-8)2+3
Answers
GPT 3.5
To find the transformations applied to the function g(x), we can compare it to the original function f(x) = x^2.
First, let's focus on the expression inside the parentheses: (x-8). This expression represents a horizontal translation of 8 units to the right. So, g(x) is shifted 8 units to the right compared to f(x).
Next, let's consider the expression (x-8)^2. This represents a vertical compression or stretching and a reflection. The coefficient 2 compresses the graph vertically by a factor of 2 compared to f(x). The square term represents a reflection about the y-axis.
Finally, the constant term 3 shifts the graph vertically upwards by 3 units compared to f(x).
In summary, the transformations applied to f(x) = x^2 to obtain g(x) = 2(x-8)^2+3 are:
1. Horizontal translation of 8 units to the right.
2. Vertical compression by a factor of 2.
3. Reflection about the y-axis.
4. Vertical shift upwards by 3 units.
First, let's focus on the expression inside the parentheses: (x-8). This expression represents a horizontal translation of 8 units to the right. So, g(x) is shifted 8 units to the right compared to f(x).
Next, let's consider the expression (x-8)^2. This represents a vertical compression or stretching and a reflection. The coefficient 2 compresses the graph vertically by a factor of 2 compared to f(x). The square term represents a reflection about the y-axis.
Finally, the constant term 3 shifts the graph vertically upwards by 3 units compared to f(x).
In summary, the transformations applied to f(x) = x^2 to obtain g(x) = 2(x-8)^2+3 are:
1. Horizontal translation of 8 units to the right.
2. Vertical compression by a factor of 2.
3. Reflection about the y-axis.
4. Vertical shift upwards by 3 units.