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?

What is the domain of this function? 0x

What is the range of this function?

1y

The + 1 shifted the graph vertically up one.

5

Shifting the Graph of a Square Root Function

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

What is the domain of this function? 0x

What is the range of this function?

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

6

Shifting the Graph of a Square Root Function

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

What is the domain of this function? 2x

What is the range of this function?

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

7

Shifting the Graph of a Square Root Function

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

What is the domain of this function? 4x

What is the range of this function?

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

8

Shifting the Graph of a Square Root Function

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

What is the domain of this function? 0x

What is the range of this function?

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

9

Shifting the Graph of a Square Root Function

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

What is the domain of this function? 0x

What is the range of this function?

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

10

Shifting the Graph of a Square Root Function

xy2

1What does the graph of

look like? Where’s the vertex?

What is the domain of this function? 0x

What is the range of this function?

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

11

Shifting the Graph of a Square Root Function

xy 3What does the graph of

look like? Where’s the vertex?

What is the domain of this function? 3x

What is the range of this function?

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

12

Shifting the Graph of a Square Root Function

xy 2What does the graph of

look like? Where’s the vertex?

What is the domain of this function? 2x

What is the range of this function?

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

What is the domain of this function? 7x

What is the range of this function?

3y

16

Graph the equation. Then state the domain and range.

423

2 xy

What is the domain of this function? 2x

What is the range of this function?

4y

17

Graph the equation. Then state the domain and range.

32 xy

What is the domain of this function? 2x

What is the range of this function?

3y

18

Graph the equation. Then state the domain and range.

533 xy

What is the domain of this function? 3x

What is the range of this function?

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

Graph & state the domain and range.

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

Graph & state the domain and range.

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