Question

Which ordered pairs lie on the graph of the exponential function f(x)=8(1/5)^x ?

(-2,80)

(1,1.6)

(0,8)

(-1,-40)

Answer 1

(1, 1.6)

(0, 8)

Explanation:

Given exponential function:

`f(x)=8\left((1)/(5)\right)^x`

Given ordered pairs:

• (-2, 80)
• (1, 1.6)
• (0, 8)
• (-1, -40)

To determine which of the given ordered pairs lie on the graph of the given exponential function, substitute each x-coordinate into the function and compare the y-coordinate.

`\begin{aligned}x=-2 \implies y&=8\left((1)/(5)\right)^(-2)\\&=8(25)\\&=200\end{aligned}`

As (-2, 200) ≠ (-2, 80) the ordered pair (-2, 80) does not lie on the graph.

`\begin{aligned}x=1 \implies y&=8\left((1)/(5)\right)^(1)\\&=8\left((1)/(5)\right)\\&=1.6\end{aligned}`

As (1, 1.6) = (1, 1.6) the ordered pair (1, 1.6) does lie on the graph.

`\begin{aligned}x=0 \implies y&=8\left((1)/(5)\right)^(0)\\&=8(1)\\&=8\end{aligned}`

As (0, 8) = (0, 8) the ordered pair (0, 8) does lie on the graph.

`\begin{aligned}x=-1 \implies y&=8\left((1)/(5)\right)^(-1)\\&=8(5)\\&=40\end{aligned}`

As (-1, 40) ≠ (-1, -40) the ordered pair (-1, -40) does not lie on the graph.