Radical and Rational Functions

Since I haven' t done it yet and I wanted to try.....

Radical and Rational Functions

Radical Function is a function that includes a radical with a variable in the radicand

Example:  √3x

Graphing Radical Functions

For this lesson it is important to remember the concepts that we learned during the transformations unit 2.

In the graph above transformations were done only on the y values and the x values stay the same.

It is also important to remember that the number inside the radicand in the cases above cannot be < 0.

Example:

y=2√x Vertical translation by a factor of 2

y= -2√x Vertical translation by a factor of 2 and reflection on the x axis

Solving the Equation of Radical and Linear Functions

G(x) = x-5

We can solve this by using the table of values. Since there is no radicand there is no restriction on the domain and range of the function.

F(x) = (√x-3)

There is a restriction on the domain since the value inside the radicand cannot be less than 0.

 x≥3

Another way to solve this is algebraically.

x-5 = (√x-3)

1.      Square both sides to get rid of the radicand symbol in f(x).

(x-5)² = x-3

2.      Square the equation (x-5)².

x²-10x+25 = x-3

3.      Solve for x.

x²-11x+28 = 0

(x-7)(x-4) = 0

(x-7) =0  or   (x-4) = 0

x= 7    or x= 4

Check to see if the solutions are correct.

x-5=(√x-3)                                 x=4

x=7                                       4-5=(√4-3)

7-5=(√7-3)                               -1=√1

2=√4                                        -1≠1

2=2

Thank you for a great class and semester, Mr.P!

Converting logarithmic functions to  

exponential logarithmic functions

In class, we learned how to convert logarithmic functions into 

exponential logarithmic functions using Mr. P's "7 Rule"method.

For example,

Evaluate:

Solution:

 By using Mr. P's seven rule method, we know that:
-3 is the new base
-"x" becomes an exponent and 81 is the answer

Final Answer: