Question

use the following information to answer the next question
the graph of the function ( y = sqrt{x} ) is transformed to the graph of ( y - k = asqrt{b(x - h)} ), where the parameters ( a, b, h, ) and ( k ) are all real numbers.
the graph has undergone the following transformations:
a vertical stretch about the ( x )-axis by a factor of 2
a vertical reflection across the ( x )-axis
a horizontal stretch about the ( y )-axis by a factor of ( \frac{1}{3} )
a horizontal translation 4 units right
a vertical translation 5 units down

reference number	possible parameters for ( a, b, h ) and ( k )
2	-2
3	3
4	-3
5	4
6	-4
7	5
8	-5

numerical response

1. complete the statements below.

the value for parameter ( \boldsymbol{a} ) is ______ (record in the first column)
the value for parameter ( \boldsymbol{b} ) is ______ (record in the second column)
the value for parameter ( \boldsymbol{h} ) is ______ (record in the third column)
the value for parameter ( \boldsymbol{k} ) is ______ (record in the fourth column)
(record your answer in the numerical - response section on the answer sheet.)

Explanation:

Step1: Find parameter $a$

Vertical stretch (factor 2) + x-axis reflection: $a = -2$

Step2: Find parameter $b$

Horizontal stretch by $\frac{1}{3}$: $b = \frac{1}{\frac{1}{3}} = 3$

Step3: Find parameter $h$

Horizontal translation 4 units right: $h = 4$

Step4: Find parameter $k$

Vertical translation 5 units down: $k = -5$

Answer:

The value for parameter $a$ is $\boldsymbol{-2}$
The value for parameter $b$ is $\boldsymbol{3}$
The value for parameter $h$ is $\boldsymbol{4}$
The value for parameter $k$ is $\boldsymbol{-5}$