Question

1. if the function ( f(x) = x^2 ) has the domain ( {0, 1, 4, 9} ) what is its range?

a) ( {0, 1, 2, 3} )
b) ( {0, 1, 16, 81} )
c) ( {0, -1, -2, -3, 3} )
d) ( {0, -1, 1, -16, -81, 81} )

1. if the domain of the function ( f(x) = 2x^2 - 8 ) is ( {-2, 3, 5} ), then the range is:

a) ( {-16, 4, 92} )
b) ( {-16, 10, 42} )
c) ( {0, 10, 42} )
d) ( {0, 4, 92} )

Explanation:

Question 3

Step 1: Recall the function and domain

The function is \( f(x) = x^2 \) and the domain is \( \{0, 1, 4, 9\} \). We need to find the range, which is the set of all output values ( \( f(x) \) values) for the given input values (domain values).

Step 2: Calculate \( f(x) \) for each domain value

• For \( x = 0 \): \( f(0) = 0^2 = 0 \)
• For \( x = 1 \): \( f(1) = 1^2 = 1 \)
• For \( x = 4 \): \( f(4) = 4^2 = 16 \)
• For \( x = 9 \): \( f(9) = 9^2 = 81 \)

Step 3: Determine the range

The range is the set of these output values: \( \{0, 1, 16, 81\} \)

Step 1: Recall the function and domain

The function is \( f(x) = 2x^2 - 8 \) and the domain is \( \{-2, 3, 5\} \). We need to find the range by calculating \( f(x) \) for each domain value.

Step 2: Calculate \( f(x) \) for each domain value

• For \( x = -2 \): \( f(-2) = 2(-2)^2 - 8 = 2(4) - 8 = 8 - 8 = 0 \)
• For \( x = 3 \): \( f(3) = 2(3)^2 - 8 = 2(9) - 8 = 18 - 8 = 10 \)
• For \( x = 5 \): \( f(5) = 2(5)^2 - 8 = 2(25) - 8 = 50 - 8 = 42 \)

Step 3: Determine the range

The range is the set of these output values: \( \{0, 10, 42\} \)

Answer:

b) {0, 1, 16, 81}

Question 4