2.53 ### Function Notation and TransformationThis section will help you understand how to write the function \( g(x) \) in terms of another function \( f \) using function notation.#### Graphical RepresentationOn the image, there are two graphs depicted on a Cartesian plane:1. **First Graph** (left side): - The graph shows a function that increases steeply from negative to positive values as \( x \) approaches 0 from the left and increases steeply from negative to positive values as \( x \ approaches 0 from the right at the origin. - X-axis range: -10 to 10 - Y-axis range: -10 to 102. **Second Graph** (right side): - The graph shows a function that decreases rapidly from positive to negative values as \( x \) approaches 0 from the left and increases rapidly from positive to negative values as \( x \) approaches 0 from the right. - X-axis range: -10 to 10 - Y-axis range: -10 to 10#### Problem Statement(d) Use function notation to write \( g \) in terms of \( f \).\[ g(x) = -f(\_\_\_\_\_\_\_\_\_\_) \]#### Additional ResourcesIf you need further assistance:- Click on "Read It" for a step-by-step explanation.- Click on "Watch It" for a video tutorial.### Need Help?- **Read It**- **Watch It** ### Understanding Transformations of FunctionsThe function \( g \) is related to one of the parent functions.\[ g(x) = -(x + 1)^3 \]#### (a) Identify the parent function \( f \):\[ f(x) = \]#### (b) Describe the sequence of transformations from \( f \) to \( g \): (Select all that apply.)- [ ] horizontal shrink- [ ] vertical shift of 1 unit downward- [ ] vertical shrink- [ ] horizontal shift of 1 unit to the left- [ ] reflection in the x-axis#### (c) Sketch the graph of \( g \).There are two graphs shown in this section. Each graph is labeled with \( y \) on the vertical axis and \( x \) on the horizontal axis. The graphs illustrate the transformation of the \( f \) function to \( g \).- **First graph:** The graph shows a function progressing downward, then sharply turning upward, depicting a cubic function that has been reflected on the x-axis and shifted horizontally. ![Graph 1](graph1.png)- **Second graph:** Similarly to the first graph, this one also illustrates a cubic function that is flipped downward and shows a horizontal shift to the left. ![Graph 2](graph2.png)#### (d) Use function notation to write \( g \) in terms of \( x \):This section is incomplete and typically would require the user to write the transformed function in proper mathematical notation.

Given function is g(x)=-(x+1)3 (1) Solution a: Parent function of (1) is f(x)=x3

The function g is related to one of the parent functions. g(x) = -(x + 1)³ (a) Identify the parent function f. f(x) = (b) Describe the sequence of transformations from f to g. (Select all that apply.) O horizontal shrink Overtical shift of 1 unit downward vertical shrink horizontal shift of 1 unit to the left reflection in the x-axis (c) Sketch the graph of g.