algebra 2 6.5

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Slide 1:

1. f(x) = 2x – 5. ANSWER ANSWER domain and range: all real numbers 2. g(x) = –x2 + 6 State the domain and range of the function. domain: all real numbers: range: y ≤ 6 BellRinger WarmUps

Graph of the Square Root :

Graph of the Square Root Remember we can’t have a negative number under an even radical so the Domain is x ≥ 0

Graph of the Cube Root :

Graph of the Cube Root Note: Since the index number is odd, we can graph the function for all x values. Therefore, the domain is all reals.

Slide 6:

EXAMPLE 1 Graph a square root function SOLUTION Domain: x ≥ 0 Range: y ≥ 0 The graph is shrunk by a factor of ½

Slide 7:

EXAMPLE 2 Graph a cube root function SOLUTION Domain: x € R Range: y € R The graph is reflected across the x axis and stretched by a factor of 3

Slide 8:

GUIDED PRACTICE for Examples 1, 2 and 3 SOLUTION

Slide 9:

GUIDED PRACTICE for Examples 1, 2 and 3

Slide 10:

Shift left 3 units. Stretch vertically by a factor of 2. Reflects about the x-axis. Vertical shift up one unit. Tranformations of radical function graphs

Slide 11:

EXAMPLE 4 Graph a translated square root function 1. Shift right 3 units 2. Stretch by factor of 2 3. Reflect across x axis 4. Shift up 2 units Domain: x ≥ 3 Range: y ≤ 2

Slide 12:

EXAMPLE 4 Graph a translated cube root function 1. Shift left 4 units 2. Stretch by factor of 3 3. Shift down 1 unit Domain: x € R Range: y € R 3

Slide 13:

GUIDED PRACTICE for Examples 4 and 5 Graph the function. Then state the domain and range.

Slide 14:

GUIDED PRACTICE for Examples 4 and 5 Graph the function. Then state the domain and range.

Homework 6.5 :

Homework 6.5 Pages: 449 – 451 Exs. 6, 8, 10, 12, 16, 20, 24, 28, 32, 41, 42