Questions: Which of the following correctly identifies the transformations undergone from f(x)=x^2 to 4 f(x+3)=4(x+3)^2 ?(1 point ) translated to the right and compressed vertically translated to the left and stretched vertically translated to the left and compressed vertically translated to the right and stretched vertically

Which of the following correctly identifies the transformations undergone from

f(x)=x^2 to

4 f(x+3)=4(x+3)^2 ?(1 point )

translated to the right and compressed vertically

translated to the left and stretched vertically

translated to the left and compressed vertically

translated to the right and stretched vertically

Transcript text: AA Senior Succe... Geretzael Al... 1001380 EN... LESSON 2 Back to Intro Page UNIT 2 Function Analysis Function Transformations Function Transformations Quick Check Which of the following correctly identifies the transformations undergone from \[ \begin{array}{l} f(x)=x^{2} \text { to } \\ 4 f(x+3)=4(x+3)^{2} ?(1 \text { point }) \end{array} \] translated to the right and compressed vertically translated to the left and stretched vertically translated to the left and compressed vertically translated to the right and stretched vertically

Solution

Solution Steps

Step 1: Identify the transformations in the function

The original function is \( f(x) = x^2 \). The transformed function is \( 4f(x+3) = 4(x+3)^2 \).

Step 2: Analyze the horizontal transformation

The term \( (x+3) \) inside the function indicates a horizontal shift. Specifically, \( f(x+3) \) represents a shift of the graph of \( f(x) \) to the left by 3 units.

Step 3: Analyze the vertical transformation

The coefficient \( 4 \) outside the function \( f(x+3) \) indicates a vertical stretch. Specifically, multiplying the function by 4 stretches the graph vertically by a factor of 4.

Step 4: Combine the transformations

The function \( 4(x+3)^2 \) undergoes a horizontal shift to the left by 3 units and a vertical stretch by a factor of 4. Therefore, the correct transformation is "translated to the left and stretched vertically."