How are the graphs of y = sin(x) and y = sin(x - 8) related? * There is a vertical shift
There is a change in the period of the function
There is a horizontal shift
There is a change in amplitude

There is a horizontal shift.

Step-by-step explanation:

Replacing  x  in a function formula with  x - 8  moves the graph 8 units to the right.

In the attached image, y = sin(x) is light green,  y = sin(x - 8) is dark green, and the arrows show how points on sin(x) get moved 8 units to the right.

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

it would be a on edgenuit y

the diagram below is your final answer