How do I horizontally translate a trigonometric graph?

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How do I horizontally translate a trigonometric graph?

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Answer 1 · 2014-11-17T00:46:51

By changing the "c" in your basic trigonometric equation.

The standard trig equation for sine is $y = a \cdot sin [b (x - c π)] + d$ $y=a*sin[b(x-cpi)]+d$ . In this, the variable $a$ $a$ represents the amplitude. The variable $b$ $b$ represents the period ( $\frac{2 π}{b}$ $(2pi)/b$ = period). Now, the variable $c$ $c$ represents what is known as the phase shift - more commonly known as a horizontal translation. You shift the graph $c π$ $cpi$ units from the original parent function, which in this case is $y = sin x$ $y=sinx$ . If $c$ $c$ is positive, shift the graph to the right $c π$ $cpi$ unites. If $c$ $c$ is negative, shift the graph to the left $c π$ $cpi$ units.

If you're wondering, $d$ $d$ represents the vertical translation.

I hope this helps, and I'f strongly suggest going to google and typing in functions like $y = sin (x - 2 π)$ $y=sin(x-2pi)$ and comparing them to the parent function, $y = sin x$ $y=sinx$ .

Answer 2 · 2014-11-17T04:17:58

Generally speaking, if you have a function $y = f (x)$ $y=f(x)$ and know its graph, the function $y = f (x - c)$ $y=f(x-c)$ has a graph that is similar to the one of $y = f (x)$ $y=f(x)$ but shifted by $c$ $c$ to the right for $c > 0$ $c>0$ or to the left for $c < 0$ $c<0$ .

Continuing the graph transformation, the graph of $y = f (x) + d$ $y=f(x)+d$ is similar to the graph of $y = f (x)$ $y=f(x)$ but shifted by $d$ $d$ up for $d > 0$ $d>0$ or down for $d < 0$ $d<0$ .

Next transformation is related to a graph of a function $y = a \cdot f (x)$ $y=a*f(x)$ . The graph of this function can be obtained from a graph of $y = f (x)$ $y=f(x)$ by stretching (if $| a | > 1$ $|a|>1$ ) or squeezing (if $| a | < 1$ $|a|<1$ ) it by a factor $a$ $a$ vertically. That is, point $(x, y)$ $(x,y)$ on a graph of $y = f (x)$ $y=f(x)$ is transferred into $(x, a \cdot y)$ $(x,a*y)$ on a graph of $y = a \cdot f (x)$ $y=a*f(x)$ . This includes reflection relative to the X-axis for $a < 0$ $a<0$ .

Finally, the graph of a function $y = f (b \cdot x)$ $y=f(b*x)$ can be obtained from the graph of $y = f (x)$ $y=f(x)$ by horizontal squeezing (if $| b | > 1$ $|b|>1$ ) or stretching (if $| b | < 1$ $|b|<1$ ) it by a factor of $b$ $b$ . That is, point $(x, y)$ $(x,y)$ on a graph of $y = f (x)$ $y=f(x)$ is transferred into $(\frac{x}{b}, y)$ $(x/b,y)$ on a graph of $y = f (b \cdot x)$ $y=f(b*x)$ . This includes reflection relative to the Y-axis for $b < 0$ $b<0$ .

You can find more detailed explanation of these manipulations with graphs in a lecture on Unizor following the menu items Algebra - Graphs - Transformation.

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How do I horizontally translate a trigonometric graph?

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