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Someone explain to me how to work with the vertical translation in b?

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So y = f(x) + 2 is a shift upwards vertically by 2 compared to y = f(x). This makes sense because we’re basically saying for each y coordinate calculate the function by plugging in x, then add 2. Hence each y coordinate is raised by 2. If you have y = f(x) + anything that just means you move it up by that.

For y = f(x + 2) we move the whole thing horizontally left by 2. The reason for this is we are saying that we need to add 2 to our x-value, and then plug it in. Hence the x-values that used to give certain y-values now have their y-values given by x-values two less, therefore all the x-values go down by 2.

Reply 2

brainmaster

Original post by Ndanji678

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simple rules;
y=f(x) then write down all the coordinates you can
if you are asked to draw a graph of f(x+a) then subtract a from all x coordinates and the y coordinates remain same.

if you are you asked to draw f(x-a) add a to all x coordinates and y coordinates remain same

asked to draw f(x) + a then add a to all y coordinates and x remains the same

asked to draw f(x)-a then subtract a from all y coordinates and x coordinates remain the same

asked to f(ax) then multiply all x coordinates by 1/a and y coordinates remain the same

asked to draw af(x) then multiply all y coordinates by a and x coordinates remain the same

hope I was helpful :smile: