Question

Use Desmos to match each logarithmic function transformation to its effect on the graph of the parent function. The logarithmic equations are log(x-2), 4*log(x), log(-x), log(x)+5. The effects on the graph of the parent function are shifts the graph upward vertically by 5 units, reflects the graph symmetrically across the y-axis, shifts the graph horizontally to the right by 2 units, stretches the graph vertically by a factor of 4.

Answer 1

Matches:

- log(x-2) → shifts the graph horizontally to the right by 2 units.
- 4·log(x) → stretches the graph vertically by a factor of 4.
- log(-x) → reflects the graph symmetrically across the y-axis.
- log(x)+5 → shifts the graph upward vertically by 5 units.

(Brief notes: log(x-2) has domain x>2; log(-x) is defined for x<0 and is the mirror of log(x) across the y-axis.)