28. use the graph of f(x) to graph y = f(x + 1) + 2. see example 4
28. use the graph of f(x) to graph y = f(x + 1) + 2. see example 4
Answer
Explanation:
Step1: Identify horizontal shift
The transformation $y = f(x + 1)$ shifts the graph of $y = f(x)$ 1 unit to the left. For a point $(x_0,y_0)$ on $y = f(x)$, the corresponding point on $y = f(x + 1)$ is $(x_0-1,y_0)$.
Step2: Identify vertical shift
The transformation $y = f(x + 1)+2$ shifts the graph of $y = f(x + 1)$ 2 units up. So the point $(x_0 - 1,y_0)$ on $y = f(x + 1)$ corresponds to the point $(x_0-1,y_0 + 2)$ on $y=f(x + 1)+2$.
Answer:
To graph $y = f(x + 1)+2$, take each point $(x,y)$ on the graph of $f(x)$, move it 1 unit to the left and 2 units up. For example, if a point on $f(x)$ is $(2,3)$, the corresponding point on $y = f(x + 1)+2$ is $(2 - 1,3 + 2)=(1,5)$. Repeat this process for all key - points on the graph of $f(x)$ (such as intercepts, maxima, minima) and then connect the new points to obtain the graph of $y = f(x + 1)+2$.