Thread: Shifting values on a graph

Hi all,

Please see attached graph. If the function represents x(t), assuming x is the x axis, how would this alternation shift or stretch the graph:

x(t -1) ?

Thanks,

Kim

horizontal shift, 1 unit to the right.

Hey thanks for the response.

So then if I have x(2-t), then t=-x+2.

Would this mean that I flip the graph about the x axis and shift the whole thing to the right by 2 units?

Also, for x(2t + 1), then t = x/2 - 1/2

Would this mean that I compress the t values by 1/2 and shift the graph 1/2 unit to the left?

Thanks,

Kim

So then if I have x(2-t), then t=-x+2.

Would this mean that I flip the graph about the x axis and shift the whole thing to the right by 2 units?

x(-t) is a reflection of the graph of x(t) over the y-axis.

x(-t+2) = x(2-t) is the graph of x(-t) horizontally shifted left 2 units.

Also, for x(2t + 1), then t = x/2 - 1/2

x(2t + 1) = x[2(t + 1/2)], which is a vertical stretch of the graph of x(t) by a factor of two with a horizontal shift left 1/2 unit.

x(2t + 1) = x[2(t + 1/2)], which is a vertical stretch of the graph of x(t) by a factor of two with a horizontal shift left 1/2 unit.

Skeeter,

Thanks for your responses. I understand the vertical stretch of the graph by a factor of two, but in the factored form doesn't the 2 carry into the 1/2 value making the leftward shift a value of 1?

Thanks,

Kim