# How do you translate a rational function?

Space and AstronomyContents:

## How do you translate rational functions?

A rational function in the form y = a/(x – h) + k is a translation of the graph y = a/x, where a translation is **the sliding of a graph along a straight line**. Both h and k in y = a/(x – h) + k give us vital information we can use to graph the function.

## How do you translate a rational function to the left?

Video quote: *Notice when C is positive the graph is shifted to the left which means we'd have X plus a constant in the denominator. So if C is positive the graph is shifted. Left.*

## How do you translate a function?

**Summary**

- To horizontally translate a function, substitute ‘x-h’ for ‘x’ in the function.
- The value for ‘h’ controls how much the graph shifts to the left or right.
- In our example, since h = -4, the graph shifts 4 units to the left.
- To vertically translate a function, add ‘k’ onto the end.

## How do you translate a rational function horizontally?

A graph is translated horizontally by **subtracting a number from the input of the function rule**. Note that the number, h, is subtracted and not added. This is so that a positive h leads to a translation to the right, which is the positive x-direction.

## What is the order for transformations?

Video quote: *You can write horizontal translation first and then vertical. Or you can do vertical translation first and then horizontal. And on the other hand you can do vertical stretches.*

## How do you graph a rational function?

**Graphing Rational Functions**

- Find the asymptotes of the rational function, if any.
- Draw the asymptotes as dotted lines.
- Find the x -intercept (s) and y -intercept of the rational function, if any.
- Find the values of y for several different values of x .
- Plot the points and draw a smooth curve to connect the points.

## How do you find a rational equation?

A rational equation is **an equation containing at least one fraction whose numerator and denominator are polynomials**, \frac{P(x)}{Q(x)}. Q(x)P(x). These fractions may be on one or both sides of the equation.

## How do you find the equation of a rational function?

Video quote: *The highest degree term would be x. Squared. If we were multiplying off the denominator the highest degree term would also be x squared. So the degree of the numerator and denominator are both 2.*

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