Algebraic Reasoning Mid-ch 3

Look at the graph below. Which of the graphs below represents the graph of the inverse of the function?

• Graph with points (6, 3), (-3, 0), and (-9, -2)

• Graph with points (3, -6), (0, 3), and (-2, 9)

• Graph with points (-6, 3), (3, 0), and (9, -2)

• Graph with points (6, -3), (3, 0), and (9, 2)

Which of the following represents f⁻¹(x), the inverse of the function f(x) = (1/2)x + 8?

• f⁻¹(x) = (x - 8) / 2

• f⁻¹(x) = (x + 8) / 2

• f⁻¹(x) = 2(x - 8)

• f⁻¹(x) = 2(x + 8)

Which of the following represents f⁻¹(x), the inverse of the function f(x) = -3(4x - 1)² + 3?

• B

• A

• C

• D

The graph of f(x) is shown below. Which of the following is a graph of the inverse of f(x)?

• Option A

  wrong

• Option B

  Correct

• Option C

  wrong

• Option D

  Wrong

The table below contains values of the function \( f(x) \). Which of the following tables represents the inverse of \( f(x) \)?

• Table A

• Table B

• Table C

• Table D

The graph of f(x) is shown below. Which of the following points would be contained in the inverse of f(x)?

• (6, 3)

• (-6, -3)

• (-3, 6)

• (-3, -6)

Which of the following functions best represents the inverse of the quadratic function h(x) = (x + 1)² + 2 when its domain is restricted to {x | x ≤ 1}?

• g(x) = -√(x - 2) - 1

• g(x) = √(x - 2) - 1

• g(x) = √(x + 1) + 2

• g(x) = -√(x + 1) + 2

Which of the following sets of tables indicates that the function f(x) and the function g(x) are inverses?

• A

• B

• C

• D

These two functions are represented on the graph: $ f(x) = x^2 + 2 $ and $ g(x) = \sqrt{x - 2} $. Which of the following is NOT true about the functions?

• The y-intercept of $ f(x) $ is (0, 2).

• The x-intercept of $ g(x) $ is (2, 0).

• The domain of $ g(x) $ is \{x | x ≥ 2\}.

• The domain of $ f(x) $ is \{x | x ≥ 2\}.

Are these graphs inverses?

• yes

• no

• There is no way to tell.