Question

graph the given functions, f and g, in the same rectangular coordinate system. use the integer values of x given to the right of the functions to obtain ordered pairs. describe how the graph of g is related to the graph of f.
f(x) = sqrt{x}
g(x) = sqrt{x} - 5
x = 0, 1, 4, 9
fill in the appropriate values for f(x) and g(x). (simplify your answers.)

x	f(x)	g(x)
0

Explanation:

Step1: Calculate f(0)

Given \( f(x) = \sqrt{x} \), substitute \( x = 0 \): \( f(0) = \sqrt{0} = 0 \)

Step2: Calculate g(0)

Given \( g(x) = \sqrt{x} - 5 \), substitute \( x = 0 \): \( g(0) = \sqrt{0} - 5 = -5 \)

Step3: Calculate f(1)

Substitute \( x = 1 \) into \( f(x) \): \( f(1) = \sqrt{1} = 1 \)

Step4: Calculate g(1)

Substitute \( x = 1 \) into \( g(x) \): \( g(1) = \sqrt{1} - 5 = 1 - 5 = -4 \)

Step5: Calculate f(4)

Substitute \( x = 4 \) into \( f(x) \): \( f(4) = \sqrt{4} = 2 \)

Step6: Calculate g(4)

Substitute \( x = 4 \) into \( g(x) \): \( g(4) = \sqrt{4} - 5 = 2 - 5 = -3 \)

Step7: Calculate f(9)

Substitute \( x = 9 \) into \( f(x) \): \( f(9) = \sqrt{9} = 3 \)

Step8: Calculate g(9)

Substitute \( x = 9 \) into \( g(x) \): \( g(9) = \sqrt{9} - 5 = 3 - 5 = -2 \)

Step9: Analyze Graph Relationship

The function \( g(x) = f(x) - 5 \), so the graph of \( g(x) \) is the graph of \( f(x) \) shifted down 5 units.

Answer:

For \( x = 0 \): \( f(0) = 0 \), \( g(0) = -5 \)
For \( x = 1 \): \( f(1) = 1 \), \( g(1) = -4 \)
For \( x = 4 \): \( f(4) = 2 \), \( g(4) = -3 \)
For \( x = 9 \): \( f(9) = 3 \), \( g(9) = -2 \)
The graph of \( g \) is the graph of \( f \) shifted vertically down by 5 units.