Question

Describe the transformations from the parent function f(x)=x^2 to the function g(x)= -1(x+1)^2+5

Answer 1

Given the functions:

`\begin{gathered} f(x)=x^2 \\ g(x)=-(x_+1)^2+5 \end{gathered}`

Given that the parent function f(x) is transformed to the function g(x), to describe the transformation,

step 1: Plot the graph of the function f(x).

The graph of f(x) is as shown below:

step 2: Plot the graph of the function g(x).

The graph of the function g(x) is as shown below:

step 3: Describe the transformation in the graph of g(x) in comparison with the function f(x).

Description:

In comparison with the graph of f(x), we observe that the graph of g(x) is reflected across the x-axis, and is shifted to the left by 1 unit, and also shifted upwards by 5 units.