Question

Complete the table for the following functionGraph the function and describe what the graph looks like.y=(1/3)^xa. Increases in Quadrant Ib. Increases from left to rightc. Decreases from left to rightd. Decreases in Quadrant III

Answer 1

The graph will decrease from left to right

Explanation:

Given information

The following function is given below as

`y\text{ = (}(1)/(3))^x`

Where

y is the output of the function and x is the input of the function.

The next step is to start substituting the value of x into the function to get the value of y

When x is -3, the corresponding value of y will be

`\begin{gathered} y\text{ = (}(1)/(3))^x \\ x\text{ = -3} \\ y\text{ = (}(1)/(3))^(-3) \\ y\text{ = 1 }/\text{ }((1)/(3))^3 \\ y\text{ = 1 }/((1)/(27)) \\ y\text{ = 1 x }(27)/(1) \\ y\text{ = 27} \\ \text{when x = -3, y = 27} \end{gathered}`

When x = -2, the corresponding value of y will be

`\begin{gathered} y\text{ = (}(1)/(3))^x \\ x\text{ = -2} \\ y\text{ = (}(1)/(3))^(-2) \\ y\text{ = 1 }/((1)/(3))^2 \\ y\text{ = 1 }/\text{ }(1)/(9) \\ y\text{ = 1 x }(9)/(1) \\ y\text{ = 9} \\ \text{when x = -2 , y = 9} \end{gathered}`

When x = 2, the corresponding value of y will be

`\begin{gathered} y\text{ = (}(1)/(3))^x \\ x\text{ = 2} \\ y\text{ = (}(1)/(3))^2 \\ y\text{ = }(1)/(9) \\ \text{when x = 2, y = }(1)/(9) \end{gathered}`

When x = 3, the corresponding value of y will be

`\begin{gathered} y\text{ = (}(1)/(3))^x \\ x\text{ = 3} \\ y\text{ = (}(1)/(3))^3 \\ y\text{ = }(1)/(27) \\ \text{when x = 3, y = }(1)/(27) \end{gathered}`

The next step is to complete the table before plotting the graph of the function

The next thing is to graph the function

From the above graph, you will see that the graph decreases from left to right

Therefore, the graph will decrease from left to right