1 graphs of radical functions. 2 the graph of a square root function on your calculator, graph the...

1Graphs of Radical Functions

2

The Graph of a Square Root Function

On your calculator, graph xy

The graph should look like half of a sideways parabola with the vertex at the origin.

In fact, it is a sideways parabola.

If you start with and square both sides of the equation, you get xy 2

xy

The graph of y2 = x is the same as y = x2. They are both parabolas. The only difference is the y2 = x opens right instead of up.

3

The Graph of a Square Root Function

The graph of does not include the bottom half of the parabola. This part is excluded, so that the graph will be a function.

xy

What is the domain of this function? 0x

What is the range of this function?

0y

4

Shifting the Graph of a Square Root Function

The graph of has a vertex at the origin and opens right.

xy

1 xyWhat does the graph of look like? Where’s the vertex?



1y

The + 1 shifted the graph vertically up one.

5





5y The - 5 shifted the graph vertically down five.

6





0y The + 2 shifted the graph horizontally two to the left.

7





0y The -4 shifted the graph horizontally four to the right.

8


xy What does the graph of look like? Where’s the vertex?



0y The minus sign in front made the graph go down.

9


xy 2What does the graph of look like? Where’s the vertex?



0y The 2 in front made the graph go up twice as fast (made it steeper).

10


xy2

1What does the graph of

look like? Where’s the vertex?



0y The 1/2 in front made the graph go up half as fast (made it less steep).

11


xy 3What does the graph of




0y The horizontal shift is 3 and the negative in front of the x makes it open left.

12


xy 2What does the graph of




0yThe horizontal shift is 2 to the left and the negative in front of the x makes it open left.

13

Vertex Form of a Radical Function

The vertex form of a radical function is:

khxay

The sign of the coefficient makes it go up or down.

The coefficient determines the steepness of the graph (like a slope)

Whatever makes the inside of the radical equal zero is the horizontal shift.

The k is the vertical shift.

The sign of the x makes it open left or right.

14

Vertex Form of all the Functions that you have learned.

The vertex form of a absolute value function is:

khxay The vertex form of a quadratic function is:

khxay 2

The vertex form of a radical function is:

khxay

15

Graph the equation. Then state the domain and range.

372 xy



3y

16


423

2 xy



4y

17


32 xy



3y

18


533 xy



5y

19

Graphs of Cube Roots Functions

Why does the cube root function have points on both sides of the y axis but the square root function does not?

Domain:

Range:

x(all real numbers)

y(all real numbers)

What does the graph of look like?3 xy

20

Graph & state the domain and range.

532 3 xyvertex at (3,5)

the coefficient is positive so the graph goes up

the 2 makes it twice as steep as a regular graph.

Domain:

Range:

x(all real numbers)

y(all real numbers)

21

Graphs of cube root functions

Vertex form of a cube root function is:

khxay 3

The sign of the coefficient makes it go up or down.

The coefficient determines the steepness of the graph (like a slope)

Whatever makes the inside of the radical equal zero is the horizontal shift.

The k is the vertical shift.

The sign of the coefficient of x makes it open left or right.

Note: the signs of the 2 coefficients may cancel either out.

22


642

1 3 xy

vertex at (-4,-6)

the coefficient is negative so the graph goes down

the 1/2 makes it half as steep as a regular graph.

Domain:

Range:

x(all real numbers)

y(all real numbers)

23


253 xyvertex at (5,2)

the coefficient is negative so the graph goes down

the negative in front of the x makes the direction of the graph flip left to right.

Domain:

Range:

x(all real numbers)

y(all real numbers)

24

4 xy 3 xy Higher Degree Roots

xy

5 xy 6 xy 7 xy

25

Sketch the graph

323

1 6 xy

26

Sketch the graph

753 19 xy

1 graphs of radical functions. 2 the graph of a square root function on your calculator, graph the...

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