Question

The graph of g(x) is a transformation of the graph of f(x)=3x 

Answer 1

There are four types of transformations of an image on a graph: translation, rotation, reflection, and dilation.

If the image moved across the graph without changing its shape, form, or tilt, it is a translation. Basically without changing form it slid from one place to another.

If the image rotated across the graph, such as switching upside-down from the first quadrant to the second, it is a rotation.

If the image moved across the graph and is in the exact opposite form as it started in (like a mirror,) it is a reflection.

If the image grew larger, it is a dilation.

Just follow the pre-image (f(x)=3x, since it started there,) to the image on your graph (g(x), since it ended there) to find out which transformation it is.

Answer 2

Answer:

The given graph is : f(x) = $3^x$

The  graph g(x) is transformation of graph f(x).

The curve g(x) passes through (-2,2) and (-1,4).

Let (a,b) be any point on f(x).After translation  new curve g(x) is obtained which is parallel to line, y=1 or asymptode is ,y=1 or when y becomes 1 the graph becomes parallel to x axis.

g(x)= y-1=$3^{x+2}$

g(x) = y = $3^{x+2} +1$ is the graph of translated curve.

The two graph is depicted below.