6. sketch a new function g(x) that is defined by g(x)=h(x)+t(x)

Explanation:

Step1: Select key - points

Select key - points on $h(x)$ and $t(x)$ such as intersection points with axes and turning points.

Step2: Add y - values

For each $x$ value of the key - points, add the corresponding $y$ - values of $h(x)$ and $t(x)$ i.e., $g(x)=h(x)+t(x)$.

Step3: Plot new points

Plot the new points obtained from the addition of $y$ - values on the coordinate plane.

Step4: Sketch the function

Connect the new points smoothly to sketch the graph of $g(x)$.

Answer:

Sketch the graph of $g(x)$ by following the above steps.