Question

GRAPH THE FUNCTION AND PLOT ONE POINT AND TELL EXACTLY WHERE IT IS

Answer 1

To graph an exponential function:

`f(x)=((1)/(5))\placeholder{⬚}^(-x+1)`

1. Use the equation to find few points in the graph:

`\begin{gathered} When\text{ x=-1} \\ f(-1)=((1)/(5))\placeholder{⬚}^(-(-1)+1)=((1)/(5))\placeholder{⬚}^2=0.04 \\ Point\text{ \lparen-1,0.04\rparen} \end{gathered}`
`\begin{gathered} When\text{ x=0} \\ f(0)=((1)/(5))\placeholder{⬚}^(-0+1)=((1)/(5))\placeholder{⬚}^1=(1)/(5)=0.2 \\ Point\text{ \lparen0,0.2\rparen} \end{gathered}`
`\begin{gathered} When\text{ x=1} \\ f(1)=((1)/(5))\placeholder{⬚}^(-1+1)=((1)/(5))\placeholder{⬚}^0=1 \\ Point\text{ \lparen1,1\rparen} \end{gathered}`
`\begin{gathered} When\text{ x=2} \\ f(2)=((1)/(5))\placeholder{⬚}^(-2+1)=((1)/(5))\placeholder{⬚}^(-1)=5 \\ Point\text{ \lparen2,5\rparen} \end{gathered}`

2. Identify the slope, using the points above you can see that the function is increasing (when x increases, y also increases)

3. Identify the end behavior:

As x increases y approaches to infinite

As x decreases y aproaches to 0, the horizontal asymptote is the x-axis

4. Graph:

Use the information you get in previous steps to graph:

5. Identify domain and range.

The domain of a function is the set of x-values for which the function is defined

The range of a function is the y-values that the function takes

For the given function:

Domain: All real numbers

`(-\infty,\infty)`

Range: All y greater than 0

`(0,\infty)`