Single Variable Calculus, Chapter 1, 1.3, Section 1.3, Problem 4

Below is the graph of function $f$. Draw the graphs of the following function.




a. $y=f(x+4)$
The graph is shifted 4 units to the left as shown in the figure below:



b. $y=f(x) + 4$
The graph is shifted 4 units upward as shown in the figure below:



c. $y=2f(x)$
The graph is stretched vertically by a factor of 2 as shown in the figure below



d. $y= -\left(\frac{1}{2}\right)f(x) + 3$
The graph is compressed vertically by a factor of 2 then it is reflected about $x$-axis and the result is shifted 3 units upward as shown in the figure.