Determine the function which corresponds to the given graph.
the asymptote is x = -3.

y = log (x + 3)

Step-by-step explanation:

This function (graph) is a translated version of the log function.

The basic graph of y = log(x) is attached.

As we can compare, we see that the basic logx graph goes through (1,0) and the asymptote is x = 0

This graph, is basically translated 3 units left, so the point becomes (1-3,0) = (-2,0) and the asymptote becomes x = -3.

THis conforms with the graph shown.

Thus, we need to horizontally translate y = log x 3 units left, which means:

y = log (x + 3)

Note: if we have a horizontal translation of a units to the left, y = logx becomes y = log(x+a)

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: