Question

use the graph of ( y = f(x) ) shown to the right to graph the following function g.
( g(x)=f(x)+1 )

Explanation:

Step1: Understand the transformation

The function \(g(x)=f(x)+1\) is a vertical shift of the function \(y = f(x)\). The rule for a vertical shift is: if \(y = f(x)\) and \(y=f(x)+k\), when \(k>0\), the graph of \(y = f(x)\) is shifted up by \(k\) units. Here \(k = 1\).

Step2: Shift each key - point

Take the key - points of \(y = f(x)\): \((-5,0)\), \((0, - 6)\), \((5,-6)\).
For the point \((x,y)\) on \(y = f(x)\), the corresponding point \((x,y + 1)\) on \(y=g(x)\).

• For the point \((-5,0)\) on \(y = f(x)\), the corresponding point on \(y=g(x)\) is \((-5,0 + 1)=(-5,1)\).
• For the point \((0,-6)\) on \(y = f(x)\), the corresponding point on \(y=g(x)\) is \((0,-6 + 1)=(0,-5)\).
• For the point \((5,-6)\) on \(y = f(x)\), the corresponding point on \(y=g(x)\) is \((5,-6+1)=(5,-5)\).

Step3: Plot the new points and draw the graph

Plot the points \((-5,1)\), \((0,-5)\), \((5,-5)\) and connect them with line - segments (since the original function \(y = f(x)\) is composed of line - segments) to get the graph of \(y = g(x)=f(x)+1\).

Answer:

Plot the points \((-5,1)\), \((0,-5)\), \((5,-5)\) and connect them to graph \(y = g(x)\).