Power and Radical Functions

We will analyze the square root functions and determine its attributes.
I will summarize the process to finding important attributes of the square root function.
TEKS 2A.2A

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Lesson 12 Attributes of Square Root functions

Open Ended

Define what a radical symbol in mathematics is: √

Consider the following...

What is the difference between the square root of 16 and 4 squared?


What's the difference between an exponent and a radical?

Open Ended

What do you think will happen if we put the variable x under the radical? What type of graph do you hypothesize will occur?

Let's make sure we understand what the radical actually means and its purpose.

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Before creating a function ...

Open Ended

Why do the square roots of any positive number have a postive AND a negative root?

Let's suppose...

Open Ended

When we created the function, $$f\left(x\right)=\sqrt[]{x}$$ , why couldn't we use the negative numbers on the x-axis?

What is the domain of this function? Is there a rule we can use for always finding the domain?

Domain - "x"

​What is the range of this type of function?

Range - "y"

Is there anyway we can fold or rotate this graph to create symmetry?

Symmetries

We can look between a set of x-values for an interval to find a local maximum (largest y-value) and a local minimum (smallest y-value)

Max/Min

Open Ended

Summarize the function that we created today and the attributes it exhibits.