Question

10 in coordinate notation: match the correct transformation compared to the parent function ( f(x) = |x| ). then describe the transformation. (a) part a ( g(x) = 3|x - 3| + 5 ) \\( \boldsymbol{\text{a}} ) ( (x,y) \to (x + 3, 3y + 5) ) \\( \boldsymbol{\text{b}} ) ( (x,y) \to (x - 3, 3y + 5) ) \\( \boldsymbol{\text{c}} ) ( (x,y) \to (x + 3, 3y - 5) ) (b) part b describe the transformation. \\( \boldsymbol{\text{a}} ) vsf: stretch \\( \boldsymbol{\text{b}} ) vsf: compression \\( \boldsymbol{\text{c}} ) vertex: left 3 and up 5 from the origin

Explanation:

Step1: Identify parent function

Parent function: $f(x)=|x|$, vertex at $(0,0)$

Step2: Analyze horizontal translation

For $g(x)=3|x-3|+5$, $x$ becomes $x-3$: shift right 3. So $(x,y)\to(x+3,y)$

Step3: Analyze vertical stretch

Vertical factor of 3: $y$ becomes $3y$. So $(x,y)\to(x,3y)$

Step4: Analyze vertical translation

Add 5: shift up 5. So $(x,y)\to(x,y+5)$

Step5: Combine transformations

Combine all: $(x,y)\to(x-3, 3y+5)$

Step6: Describe transformation details

Vertical stretch by factor 3, horizontal shift right 3, vertical shift up 5.

Answer:

Part A:

B. $(x,y)\to(x-3,3y+5)$

Part B:

• Vertical stretch by a scale factor of 3
• Horizontal shift 3 units to the right
• Vertical shift 5 units up

(Vertex of $g(x)$ is $(3,5)$, which is right 3 and up 5 from the parent function's vertex $(0,0)$; vertical scale factor 3 is a stretch)