Question

graph the piece - wise function given below.
f(x)=\begin{cases}4& \text{for }x < 4\\(x - 5)^2+1& \text{for }4 < xleq7end{cases}
step 1: select a function then move with blue dot (if necessary)

Explanation:

Step1: Graph $y = 4$ for $x<4$

This is a horizontal - line. The line $y = 4$ has a $y$ - value of 4 for all $x$ values less than 4. We use an open - circle at $x = 4$ to indicate that $x = 4$ is not included in this part of the domain.

Step2: Graph $y=(x - 5)^2+1$ for $4

First, identify the vertex of the parabola $y=(x - 5)^2+1$. The vertex form of a parabola is $y=a(x - h)^2+k$, where $(h,k)$ is the vertex. Here, $h = 5$ and $k = 1$, so the vertex is $(5,1)$.
When $x = 4$, $y=(4 - 5)^2+1=2$. We use an open - circle at $(4,2)$ since $x = 4$ is not included in this part of the domain.
When $x = 7$, $y=(7 - 5)^2+1=5$. We use a closed - circle at $(7,5)$ since $x = 7$ is included in this part of the domain. Then we draw the parabola for the domain $4

Answer:

The graph consists of a horizontal line $y = 4$ with an open - circle at $(4,4)$ for $x<4$ and a parabola $y=(x - 5)^2+1$ with an open - circle at $(4,2)$ and a closed - circle at $(7,5)$ for $4