Question

What are the coordinates points that I can plot into the graph?

Answer 1

To find points in the graph of a function you substitute the x inthe equation by specific values and find the corresponding y-value.

For the given function:

`y=((1)/(2))^(x-3)-8`

1. Find y when x=0

`y=((1)/(2))^(0-3)-8=((1)/(2))^(-3)-8=(1^(-3))/(2^(-3))-8=(2^3)/(1^3)-8=2^3-8=8-8=0`

Point (0,0)

2. Find y when x=1

`y=((1)/(2))^(1-3)-8=((1)/(2))^(-2)-8=(1^(-2))/(2^(-2))-8=(2^2)/(1^2)-8=2^2-8=4-8=-4`

Point (1,-4)

3. Find y when x=-1

`y=((1)/(2))^(-1-3)-8=((1)/(2))^(-4)-8=(1^(-4))/(2^(-4))-8=(2^4)/(1^4)=2^4-8=16-8=8`

Point (-1,8)

4. Find y when x= 2

`y=((1)/(2))^(2-3)-8=((1)/(2))^(-1)-8=(1^(-1))/(2^(-1))-8=(2)/(1)-8=2-8=-6`

Point (2,-6)

5. Find y when x=3

`y=((1)/(2))^(3-3)-8=((1)/(2))^0-8=1-8=-7`

Point (3,-7)

Then, you have the next points: (-1,8), (0,0), (1,-4), (2,-6), (3,-7)