EJU - Examination for Japanese University Mathematics: Functions and Graphs Questions and Answers

Question 1

Find the coordinates of the vertex of the parabola defined by the quadratic function y = 2x² - 8x + 5.

Accepted Answer

(2, -3)

Answer

(-2, 29)

Answer

(4, 5)

Answer

(-8, 197)

Question 2

The graph of the function y = f(x) is translated 3 units to the left and 4 units down. Which of the following equations represents the new graph?

Accepted Answer

y = f(x + 3) - 4

Answer

y = f(x + 3) + 4

Answer

y = f(x - 3) + 4

Answer

y = f(x - 3) - 4

Question 3

What is the period of the function y = 3sin(2x - π/2)?

Accepted Answer

π

Answer

2π

Answer

π/2

Answer

4π

Question 4

Which of the following statements is true about the relationship between the graph of a function y = f(x) and its inverse function y = f⁻¹(x)?

Accepted Answer

They are reflections of each other across the line y = x.

Answer

They are reflections of each other across the y-axis.

Answer

They are reflections of each other across the x-axis.

Answer

They are reflections of each other across the origin.

Question 5

A logarithmic function is given by y = log₂(x - 3). What is the domain of this function?

Accepted Answer

x > 3

Answer

x > 0

Answer

x < 3

Answer

All real numbers

Question 6

The graph of the quadratic function y = ax² + bx + c opens downwards and has two distinct x-intercepts. Which of the following must be true?

Accepted Answer

a < 0 and b² - 4ac > 0

Answer

a > 0 and b² - 4ac > 0

Answer

a > 0 and b² - 4ac < 0

Answer

a < 0 and b² - 4ac < 0