ANSWER -
The graph that represents the logarithmic function y = ln(3x + 4) + 3 is a curve that passes through the point (–1, 3) and approaches the x-axis asymptotically as x approaches –4/3.
The graph of the natural logarithmic function y = ln(x) looks like:
Logarithmic Function Graph
To obtain the graph of y = ln(3x + 4) + 3, we can apply transformations to the graph of y = ln(x):
Horizontal compression by a factor of 1/3: This squeezes the graph horizontally by a factor of 1/3, making it steeper.
Horizontal shift to the left by 4/3: This moves the graph 4/3 units to the left.
Vertical shift upwards by 3: This moves the graph 3 units up.
Therefore, the graph of the logarithmic function y = ln(3x + 4) + 3 would look like:
Logarithmic Function Graph with transformations