Intervals Quadratic

For Graph #2, over which interval is the function decreasing?

• (4, 6)

• (2, ∞)

• (0, 2)

• (-∞, 4)

Answer explanation

The function is decreasing in the interval (4, 6) as the graph shows a downward trend in this range. Other intervals either show an increase or are not relevant to the question.

What is the domain of the function?

• x > 2

• x > 3

• All Real Numbers

Answer explanation

The function has no restrictions on the values of x, meaning it can take any real number. Therefore, the domain is 'All Real Numbers', making this the correct choice.

What is the domain?

• [-2, 3]

• [-2, 3)

• (-2, 3]

• [-3, 4]

• (-3, 4]

Answer explanation

The domain is defined as the set of input values. The correct choice, (-2, 3], indicates that -2 is not included (open interval) while 3 is included (closed interval), fitting the criteria for the domain.

For Graph #1, over which interval is the function increasing?

• (-∞, 2)

• (2, ∞)

• (4, 6)

• (0, 2)

Answer explanation

The function is increasing in the interval (2, ∞) because the graph shows a positive slope starting from x = 2 onwards, indicating that the values of the function rise as x increases beyond 2.

Which of the following represents a quadratic function?

y = x² - 4x + 5

• down and down

• down and up

• up and down

• up and up

Which answer choice describes  y = -3x² +7x - 2 accurately?

• opens up with a maximum

• opens up with a minimum

• opens down with a maximum

• opens down with a minimum 

What is the range of the function?

• y ≤ -2

• y ≤ 5

• All Real Numbers

Answer explanation

The function's range is determined by its maximum value. Since the correct answer is y ≤ 5, it indicates that the function can take any value up to and including 5, making this the appropriate choice.

Which of these best represents the domain?

Answer explanation

The correct choice, -3≤x<5, accurately represents the domain by including -3 and excluding 5, which aligns with typical interval notation for domains.

What are the domain and range of the graph?

Answer explanation

The correct choice states that the domain is all real numbers, indicating the graph extends infinitely in the x-direction. The range is y≥-4, meaning the graph starts at -4 and goes upwards, confirming the correct answer.