Milestones Mixed Practice (State Questions)

The number of school buses needed to transport students on a field trip is given by the function  $f(x)=\frac{x+3}{30}$, where x represents the number of students going on the trip. What is the domain of this function?

• x is the set of all real numbers.

• x is the set of all integers.

• x is the set of all nonnegative integers.

• x is the set of all nonnegative real numbers.

Answer explanation

The correct answer is choice (C), x is the set of all nonnegative integers. Choices (A), (B), and (D) would include either fractional numbers, negative numbers, or both. The number of buses must be a positive whole number.

A scientist studied the relationship between the number of trees, x, per acre and the number of birds, y, per acre in a neighborhood. She modeled the relationship with a scatter plot and used the equation y = 4 + 6x for the regression line. What is the meaning of the slope and y-intercept of this regression line?

• The slope is 6. This means that the average number of birds per acre in an area with no trees is 6. The y-intercept is 4. This means that for every 1 additional tree, she can expect an average of 4 additional birds per acre.

• The slope is 4. This means that for every 1 additional tree, she can expect an average of 4 additional birds per acre. The y-intercept is 6. This means that the average number of birds per acre in an area with no trees is 6.

• The slope is 6. This means that for every 1 additional tree, she can expect an average of 6 additional birds per acre. The y-intercept is 4. This means that the average number of birds per acre in an area with no trees is 4.

• The slope is 4. This means that the average number of birds per acre in an area with no trees is 4. The y-intercept is 6. This means that for every 1 additional tree, she can expect an average of 6 additional birds per acre.

Answer explanation

The correct answer is choice (C). Choice (A) is incorrect because the y-intercept is being used as a rate of change. Choice (B) has the incorrect interpretation of slope within the context. Choice (D) has the incorrect interpretation of slope and y-intercept within the context.

Which value is an irrational number?

The table defines a quadratic function.

What is the average rate of change between x = –1 and x = 1?

• undefined

Answer explanation

The correct answer is choice (C) –3. Rate of change is found by finding the slope of the line containing the indicated points. Choice (A) is incorrect because it incorrectly computes the slope. Choice (B) is incorrect because it reverses the numerator and denominator in the slope formula. Choice (D) is incorrect because it incorrectly computes the slope.

• -42

• -36

• -33

• -27

Answer explanation

This is the correct response because the vertex of the function is at (3, –36).

• -9, -3

• 0, 0

• 3, -9

• -3, 9

Answer explanation

The function crosses the x-axis at (–3, 0) and (9, 0).

The function f(x) = 3x – 9 is shifted 2 units up. Which equation correctly describes the new function?

• g(x) = 6x – 9

• g(x) = 3(x + 2) – 9

• g(x) = 3x – 7

• g(x) = 6x – 18

Answer explanation

The correct answer is choice (C). g(x) = 3x – 7. A shift up 2 units would add 2 units to the function. Choice (A) is incorrect because the x-value is multiplied by 2. Choice (B) is incorrect because 2 is added to the x-value. Choice (D) is incorrect because the function is multiplied by 2.

• (–3, 4)

• (–3, ∞)

• (–∞, 4)

• (–∞, ∞)

Answer explanation

The range of all linear functions (except those in context) will always be (–∞, ∞) or all real numbers. The domain for all functions - linear, exponential and quadratic all also all real numbers.

• (0, –4)

• (0, –3)

• (0, 1)

• (0, 2)

If the parent function is f(x) = mx + b, what is the value of the parameter m for the line passing through the points (–2, 7) and (4, 3)?