Question

1. mixed function analysis consider these two functions: g(x)=3(x + 1)-4 h(x)=2(x - 3)^2+5 a) for each function: identify the parent function write out all parameters and their meanings list transformations in order of application

Explanation:

For function $g(x)=3(x + 1)-4$:

Step1: Identify parent - function

The parent function of $g(x)$ is the linear function $y = x$.

Step2: Identify parameters and meanings

The parameter $a = 3$ represents a vertical stretch by a factor of 3. The parameter $h=- 1$ represents a horizontal shift 1 unit to the left. The parameter $k = - 4$ represents a vertical shift 4 units down.

Step3: List transformations

1. Horizontal shift 1 unit to the left.
2. Vertical stretch by a factor of 3.
3. Vertical shift 4 units down.

For function $h(x)=2(x - 3)^2+5$:

Step1: Identify parent - function

The parent function of $h(x)$ is the quadratic function $y=x^{2}$.

Step2: Identify parameters and meanings

The parameter $a = 2$ represents a vertical stretch by a factor of 2. The parameter $h = 3$ represents a horizontal shift 3 units to the right. The parameter $k = 5$ represents a vertical shift 5 units up.

Step3: List transformations

1. Horizontal shift 3 units to the right.
2. Vertical stretch by a factor of 2.
3. Vertical shift 5 units up.

Answer:

For $g(x)=3(x + 1)-4$:

• Parent function: $y = x$
• Parameters: $a = 3$ (vertical stretch), $h=-1$ (horizontal shift left), $k = - 4$ (vertical shift down)
• Transformations: Horizontal shift 1 unit left, vertical stretch by factor 3, vertical shift 4 units down.

For $h(x)=2(x - 3)^2+5$:

• Parent function: $y=x^{2}$
• Parameters: $a = 2$ (vertical stretch), $h = 3$ (horizontal shift right), $k = 5$ (vertical shift up)
• Transformations: Horizontal shift 3 units right, vertical stretch by factor 2, vertical shift 5 units up.