Answer to Question #247177 in Math for john

Question

Sketch the graph of f(x)=2 log1/3 (x+4)−1 using transformation techniques. 

Answer 1

$$y_1=\log_{1/3}x$$

Shift the graph of $y_1=\log_{1/3}x$ to the left 4 units

$$y_2=\log_{1/3}(x+4)$$

Stretch the graph $y_2=\log_{1/3}(x+4)$ vertically by a factor of $2$

$$y_3=2\log_{1/3}(x+4)$$

Shift the graph of $y_3=2\log_{1/3}(x+4)$ downward 1 unit

$$y=2\log_{1/3}(x+4)-1$$