Do Now:

Write the recursive formula for the following problems or write the pattern. 1.a1= -3, an = an-1 +3

2. a1= -2, an = 2an-1

3.256, 64, 16, 4, 1 …4. 3, 7, 11, 15, 19

Objective:

• To graph square root functions.

Vocab.

• A radical expression is an expression that contains a radical sign.

• If the radical is a square root then it’s called a square root function.

Parent Square Root Function:

EXAMPLE 1

SOLUTION

STEP 1

Graph a function of the form y = a x

Graph the function y = 3 x and identify its domain and range. Compare the graph with the graph of y = x .

Make a table. Because the square root of a negative number is undefined, x must be nonnegative. So, the domain is x ≥ 0.

STEP 2

Plot the points.

EXAMPLE 1

STEP 3

Graph a function of the form y = a x

STEP 4

Draw a smooth curve through the points. From either the table or the graph, you can see the range of the function is y ≥ 0.

Compare the graph with the graph of y = x . The graph of y = 3 x is a vertical stretch (by a factor of 3) of the graph of y = x .

EXAMPLE 2 Graph a function of the form y = a x

SOLUTION

Graph the function y = –0.5 x and identify its domain and range. Compare the graph with the graph of y = x .

To graph the function, make a table, plot the points, and draw a smooth curve through the points. The domain is x ≥ 0.

The range is y ≤ 0.The graph of y = –0.5 x is a vertical shrink (by a factor of 0.5) with a reflection in the x-axis of the graph of y = x .

EXAMPLE 3 Graph a function of the form y = x + k

SOLUTION

Graph the function y = x + 2 and identify its domain and range. Compare the graph with the graph of y = x .

To graph the function, make a table, then plot and connect the points. The domain is x ≥ 0.

The range is y ≥ 2.The graph of y = x + 2 is a vertical translation (of 2 units up) of the graph of y = x .

GUIDED PRACTICE for Examples 1, 2 and 3

Graph the function and identify its domain and range. Compare the graph with the graph of y = x .

1. y = 2 x

ANSWER

Domain: x ≥ 0, Range: y ≥ 0Vertical stretch by a factor of 2

GUIDED PRACTICE for Examples 1, 2 and 3

Graph the function and identify its domain and range. Compare the graph with the graph of y = x .

2. y = x – 1

Domain: x ≥ 0, Range: y ≥ 0 – 1Vertical translation of 1 unit down

ANSWER

GUIDED PRACTICE for Examples 1, 2 and 3

Graph the function and identify its domain and range. Compare the graph with the graph of y = x .

3. y = x + 3

Domain: x ≥ 0, Range: y ≤ 0Vertical translation of 3 units up

ANSWER

EXAMPLE 4

SOLUTION

Graph a function of the form y = x – h

Graph the function y = x – 4 and identify its domain and range. Compare the graph with the graph of y = x .

To graph the function, make a table, then plot and connect the points. To find the domain, find the values of x for which the radicand, x – 4 , is nonnegative. The domain is x ≥ 4.

EXAMPLE 4 Graph a function of the form y = x – h

The range is y ≥ 0.The graph of y = x – 4 is a horizontal translation (of 4 units to the right) of the graph of y = .x

EXAMPLE 5 Graph a function of the form y = a x – h + k

x + 4Graph the function y = 2 – 1 .

SOLUTION

STEP 1

Sketch the graph of y = 2 .x

STEP 2

So, h = –4 and k = –1. Shift the graph left 4 units and down 1 unit.

y = 2 – 1 = 2 x – (–4) + (–1). x + 4

Shift the graph h units horizontally and k units vertically. Notice that

Exit Ticket for Examples 4 and 5

Graph the function y = x + 3 and identify its domain and range. Compare the graph with the graph of y = x .

Domain: x ≥ – 3; Range: y ≥ 0; Horizontal translation 3 units to the left

ANSWER

GUIDED PRACTICE for Examples 4 and 5

6. Identify the domain and range of the function in Example 5.

The domain is x ≥ – 4. The range is y ≥ –1.

ANSWER