Question

1.which transformations occur to the parent function f(x) to from g(x)=5 f(x+4)-8?

2.what transformations occur when the input value changes to its opposite
f(x) ----> -f(x)
3. Describe the transformation from the graph f(x) to the graph of g(x)
x -5, -3, -1, 1- 3
f(x) 6, 2, 0, 2, 6
g(x)=a.f(x) 3, 1, 0, 1, 3

Answer 1

The function g(x) = 5f(x+4)-8 has three transformations: a vertical translation, a horizontal translation, and a vertical scaling.

Step-by-step explanation:

The function g(x) = 5f(x+4)-8 is formed by applying three transformations to the parent function f(x). Let's break down the transformations:

Vertical Translation: The -8 in the equation shifts the graph 8 units downward.

Horizontal Translation: The +4 inside the function shifts the graph 4 units to the left.

Vertical Scaling: The 5 in front of f(x+4) stretches the graph vertically by a factor of 5. If a point on the original graph is (x, y), the corresponding point on the transformed graph will be (x, 5y).

Therefore, the transformations applied to the parent function f(x) to form g(x) are a vertical translation of -8 units, a horizontal translation of 4 units to the left, and a vertical scaling by a factor of 5.