5.03 Other rational functions
Interactive practice questions
Consider the function $f\left(x\right)=\frac{1}{x+4}$f(x)=1x+4.
How can the graph of $f\left(x\right)$f(x) be obtained from the graph of $y=\frac{1}{x}$y=1x?
Shift to the left $4$4 units.
Shift down $4$4 units.
Shift to the right $4$4 units.
Shift up $4$4 units.
Graph $f\left(x\right)$f(x).
State the domain of $f\left(x\right)$f(x) using interval notation.
State the range of $f\left(x\right)$f(x) using interval notation.
Which of the following statements are true about $f\left(x\right)$f(x) over its domain $\left(-\infty,-4\right)\cup\left(-4,\infty\right)$(−∞,−4)∪(−4,∞)?
$f\left(x\right)$f(x) is increasing over both parts of its domain.
$f\left(x\right)$f(x) is sometimes increasing and sometimes decreasing over its domain.
There is not enough information to determine whether or not $f\left(x\right)$f(x) is increasing or decreasing over its domain.
$f\left(x\right)$f(x) is decreasing over both parts of its domain.
Consider the function $f\left(x\right)=\frac{5}{x}$f(x)=5x.
Consider the function $f\left(x\right)=-\frac{1}{x}$f(x)=−1x.
Consider the function $f\left(x\right)=\frac{3}{x}$f(x)=3x.