College Algebra, Chapter 3, 3.5, Section 3.5, Problem 54

The graph of $g$ is given below. Sketch the graphs of the following functions.







a.) $y = g(x + 1)$

The graph of $y = g(x + 1)$ is the graph of $g(x)$ that is shifted 1 unit to the left.







b.) $y = g(-x)$

The graph of $y = g(-x)$ is the graph of $g(x)$ that is reflected about $y$-axis.







c.) $y = g(x - 2)$

The graph of $y = g(x - 2)$ is the graph of $g(x)$ that is shifted 2 units to the right.







d.) $y = g(x) - 2$

The graph of $y = g(x) - 2$ is the graph of $g(x)$ that is shifted 2 units downward.







e.) $y = -g(x)$

The graph of $y = -g(x)$ is the graph of $g(x)$ that is reflected about $x$-axis.







f.) $y = 2g (x)$

The graph of $y = 2g (x)$ is the graph og $g(x)$ that is stretched vertically by a factor of 2.