Example: For the function below. Graph using transformations. Find the y-intercept. State the horizontal asymptote and the domain and range.
First we must examine the base function
Graph using plotting points. We can use the standard set of x-values to find ordered pairs.
The graph below shows the points plotted and the line that connects them. This graph has a horizontal asymptote at y=0. The domain is and the range is
Analyze the transformations.
The +2 in the exponent shifts the graph left 2 units.
The – in the front of the base reflects the graph over the x-axis.
The +2 next to the base shifts the graph and the horizontal asymptote up two units.
You can see the graph after the transformations.
The horizontal asymptote is y=2. The domain is and the range is
To find the y-intercept we let x=0.
Thus the y-intercept is (0,-2)