6.8 G RAPHING R ADICAL F UNCTIONS Algebra II w/ trig.

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Presentation transcript:

6.8 G RAPHING R ADICAL F UNCTIONS Algebra II w/ trig

Inverses of the power functions y = x²( with domains restricted as needed) form parent functions for families of radical functions. In particular, f(x) = √x is the parent function for the family of square root functions. Members of this family have the general form f(x) = a√(x –h) +k Reminder: Reflection in x axis : y = - a√x or Stretch (a > 1), shrink (0<a<1)

If you understand the patterns that take place when graphing a function, then graphing becomes a quick and painless process. Let’s look at the parent graph f(x) = √x or y = √x Domain: x > 0 Range: y > 0 General equation: y = a √(x-h) + k where a, h, and k effect the placement of the graph.

General equation: y = a √(x-h) + k Again, (h, k) is your starting point of the graph, because it is where the graph has been translated to. H is your horizontal shift and K is the vertical shift. *Remember to take the opposite of h and k as you see it. Also, the a term works like the rise part of your slope and the run is always 1 (only for the first point after your starting point). You can also make a table to find more points on the graph.

I. Graph. A.B.

C.

II. Graph each cube root: Step 1. Graph the parent function. A.Step 2. Multiply the y- coordinates by 2. This stretches the graph vertically. Step 3. Translate the graph from Step2, 4 unit to the left and 1 units up.

B.

III. Rewrite each function to make it easy to graph using transformations of its parent functions. Describe the graph. A. Step 1. Factor the radicand to get in (x –h) form. Step 2. Find the root of the GCF. B.