Question

Find the domain and range of each function. Write your answer in interval notation.

f(x)=3sinx


f(x)=2/(x-1)

Answer 1

At first. \(\normalsize\color{blue}{ f(x)=3\sin(x)\LARGE\color{white}{ \rm │ }}\)
Knowing that a sine of an angle is a ratio of an opposite side to the hypotenuse of the \(\normalsize\color{blue}{ \LARGE\color{white}{ \rm │ }}\)
triangle, we know that ` │sin (anything)│≤ 1`. And therefore, we know that the range will \(\normalsize\color{blue}{ \LARGE\color{white}{ \rm │ }}\)
be not more than 3.\(\normalsize\color{blue}{ \LARGE\color{white}{ \rm │ }}\)

The domain can be any x value, because there no restrictions.

Answer 2

For \(\large\color{blue}{ f(x)=\frac{2}{x-1}\LARGE\color{white}{ \rm │ }}\), you can see that range won't be zero, right?

range can be anything other than zero, because as x→∞, y→∞ \(\large\color{blue}{ \LARGE\color{white}{ \rm │ }}\)
The domain can be anything other than a 1, because when x=1, the denominator is zero. \(\large\color{blue}{ \LARGE\color{white}{ \rm │ }}\)