Question

Use the domain {1/2, 1, 2, 4, 8, 16} and plot the six points that would satisfy the equation. Submit your graph.

Answer 1

Given:

The equation is

$y=\log_2x$

The domain is $\{\dfrac{1}2, 1, 2, 4, 8, 16\}$.

To find:

The graph of six points that would satisfy the equation.

Solution:

We have,

$y=\log_2x$

For $x=\dfrac{1}{2}$,

$y=\log_2\dfrac{1}{2}$

$y=\log_22^{-1}$

$y=-1$                          $[\because \log_aa^x=x]$

Similarly, at x=1,

$y=\log_22^0$

$y=0$

At x=2,

$y=\log_22^1$

$y=1$                      $[\because \log_aa^x=x]$

At x=4,

$y=\log_22^2$

$y=2$                      $[\because \log_aa^x=x]$

At x=8,

$y=\log_22^3$

$y=3$                      $[\because \log_aa^x=x]$

At x=16,

$y=\log_22^4$

$y=4$                      $[\because \log_aa^x=x]$

Plot the points $(\dfrac{1}{2},-1),(1,0),(2,1),(4,2),(8,3),(16,4)$ on a coordinate plane as shown below.