Graphing Exponential and logarithm function by transformation

Vertical shift

If k>0k>0 , the graph would be shifted upwards.

If k<0k<0 , the graph would be shifted downwards.

Horizontal Shift

If h>0h>0 , the graph would be shifted left.

If h<0h<0 , the graph would be shifted right.

HELPFUL HINT:

By nature of the logarithm, most log graphs tend to have the same shape, looking similar to a square-root graph:

SAT PROBLEM

Example 1:

Find the domain and range of the function y=3x+2 .

Graph the function on a coordinate plane.

The graph is nothing but the graph y=3x translated 2 units to the left.

The function is defined for all real numbers. So, the domain of the function is set of real numbers.

As x tends to ∞ , the value of the function also tends to ∞ and as x tends to −∞ , the function approaches the x -axis but never touches it.

Therefore, the range of the function is set of real positive numbers or {x∈ℝ∣∣x>0} .