Question

g(x) -1 1 7 17
x 0 1 2 3

The table above gives values of the quadratic functions g for selected values of x. Which of the following defines g.
A. g(x) = x 2 − 1
B. g(x) = x 2 + 1
C. g(x) = 2 x 2 − 1
D. g(x) = 2 x 2 E. g(x) = 3 x 2 − 2

Answer 1

g(x) = 2x² - 1 defines g ⇒ answer C

Step-by-step explanation:

The table:

→  g(x)  :   -1   :   1   :   7   :   17

→   x      :   0   :   1   :   2   :   3

The table above gives values of the quadratic functions g for

selected values of x

We need to find which of the answers defines g

To do that:

• Write the function
• Substitute x by each value of x in the table
• If all answers of g(x) is the same with corresponding values of g(x) in the table, then the function defines g(x)

A. g(x) = x² - 1

∵ x = 0

∴ g(0) = (0)² - 1 = 0 - 1 = -1

∵ x = 1

∴ g(1) = (1)² - 1 = 1 - 1 = 0

∵ g(1) in the table = 1

∴ Answer A does not define g

B. g(x) = x² + 1

∵ x = 0

∴ g(0) = (0)² + 1 = 0 + 1 = 1

∵ g(0) in the table = -1

∴ Answer B does not define g

C. g(x) = 2x² - 1

∵ x = 0

∴ g(0) = 2(0)² - 1 = 2(0) - 1 = 0 - 1 = -1

∵ x = 1

∴ g(1) = 2(1)² - 1 = 2(1) - 1 = 2 - 1 = 1

∵ x = 2

∴ g(2) = 2(2)² - 1 = 2(4) - 1 = 8 - 1 = 7

∵ x = 3

∴ g(3) = 2(3)² - 1 = 2(9) - 1 = 18 - 1 = 17

∵ The values of g(x) are the same with the values of g(x) in the table

∴ Answer C defines g

∴ g(x) = 2x² - 1 defines g

D. g(x) = 2x²

∵ x = 0

∴ g(0) =2(0)² = 2(0) = 0

∵ g(0) in the table = -1

∴ Answer D does not define g

E. g(x) = 3x² - 2

∵ x = 0

∴ g(0) = 3(0)² - 2 = 3(0) - 2 = 0 - 2 = -2

∵ g(0) in the table = -1

∴ Answer E does not define g

g(x) = 2x² - 1 defines g

Learn more:

You can learn more about quadratic functions in brainly.com/question/1357167

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