Question

Use the interactive graph below to sketch a graph of y=3^4-x + 1

Answer 1

Given:

`y=3^(4-x)+1`

To determine: the graph of the above function.

Solution:

Let us get a table for x and y using a range values for x between -4 to 4

`\begin{gathered} \text{When x = -4} \\ y=3^(4--4)+1 \\ y=3^(4+4)+1 \\ y=3^8+1=6561+1=6562 \end{gathered}`
`\begin{gathered} \text{when x = -2} \\ y=3^(4--2)+1 \\ y=3^(4+2)+1 \\ y=3^6+1=729+1=730_{} \end{gathered}`
`\begin{gathered} \text{when x = 0} \\ y=3^(4-0)+1 \\ y=3^4+1=81+1=82 \end{gathered}`
`\begin{gathered} \text{When x = 2} \\ y=3^(4-2)+1 \\ y=3^2+1=9+1=10 \end{gathered}`
`\begin{gathered} \text{When x = 4} \\ y=3^(4-4)+1 \\ y=3^0+1 \\ y=1+1=2 \end{gathered}`

The table of values of x and y is as shown below

The graph of the function through the table above is shown below:

Hence, the graph of the given function is givem above