Given a function $f(x)$, a new function $g(x)=f(x)+k$, where $k$ is a constant, is a vertical shift of the function $f(x)$. All the output values change by $k$ units. If $k$ is positive, the graph will shift up. If $k$ is negative, the graph will shift down.

Given a function $f$, a new function $g(x)=f(x-h)$, where $h$ is a constant, is a horizontal shift of the function $f$. If $h$ is positive, the graph will shift right. If $h$ is negative, the graph will shift left.

Step 1 - Identify the vertical and horizontal shifts from the formula.

Step 2 - The vertical shift results from a constant added to the output. Move the graph up for a positive constant and down for a negative constant.

Step 3 - The horizontal shift results from a constant subtracted from the input. Move the graph right for a positive constant and left for a negative constant.

Step 4 - Apply the shifts to the graph in either order.

Given a function $f(x)$, a new function $g(x)=-f(x)$ is a vertical reflection of the function $f(x)$, sometimes called a reflection about (or over, or through) the $x$-axis.

Given a function $f(x)$, a new function $g(x)=f(-x)$ is a horizontal reflection of the function $f(x)$, sometimes called a reflection about the $y$-axis.