Graphing Reciprocal Functions 1

Another lesson that we discussed is GRAPHING RECIPROCAL FUNCTIONS.

The basic graph of reciprocal functions is f(x)= 1/x.

The shifted shape is showed as f(x) = 1/ (x-h) + k.

Before graphing reciprocal functions, we need to find the Vertical Asymptote (VA) and Horizontal Asymptote (HA).

Vertical Asymptote is the value of x that makes the function undefined. In the basic form, VA is always at x=0.

Horizontal Asymptote is the value of y that is no longer able to occur due to the unacceptablevalue for x (VA). In the basic form, it is always at y=0.

• In the shifted shape, the horizontal shift (left or right) is the h value and is read as the opposite. The VA will always be at x= h.

ex. If h= 1, since we read it as the opposite, the graph will move 1 unit to the left.

• Meanwhile, the vertical shift (up or down) is the k value which is read as it is. The HA will always be at y=k.

ex. If k=13 then the shift will be 13units up.

• We should also find the domain, range, x- intercept/s, and y-intercept/s.
• If a negative is placed in front of the function, multiply all the y- values by -1.

Examples:

1. f(x)= 1/x

• VA is at x= 0.
• HA is y=0.
• Domain: x ϵ ℝ; x≠0.
• Range: y ϵ ℝ; y≠0.
• There are no x and y intercepts since both VA and HA are 0.

Graph should look like this.

2. f(x)= 1/ x+2

• VA : x= -2
• HA: y= 0
• Domain: x ϵ ℝ; x≠ -2.
• Range: y ϵ ℝ; y≠0.
• x- intercept: none
• y- intercept: y= ½

Graph should look like this.

3. f(x)= 1/ (x+4) – 2.

• VA : x= -4.
• HA: y= -2.
• Domain: x ϵ ℝ; x≠ -4.
• Range: y ϵ ℝ; y≠ -2.
• x- intercept: x= -7/2
• y- intercept: y= -7/4

The graph should look like this: