Chapter 2 Review (Honors Precalculus)

Answer explanation

To find the average rate of change of f(x) = 2x^2 + 1 from x = 0 to x = 1, calculate f(1) - f(0) = (2(1)^2 + 1) - (2(0)^2 + 1) = 3 - 1 = 2. Then divide by the interval length: 2 / (1 - 0) = 2. The correct answer is 0.

Tags

CCSS.HSF.IF.B.6

Given the graph, find the average rate of change from x = -1 to x = 2.

Answer explanation

To find the average rate of change from x = -1 to x = 2, calculate the change in y-values divided by the change in x-values. If the graph shows equal y-values at these points, the average rate of change is 0.

Tags

CCSS.HSF.IF.B.6

The function h(t) = -8t² + 24t + 32 models the approximate height of an object t seconds after it is launched. How many seconds does it take the object to hit the ground?

• 32 seconds

• 1 seconds

• 4 seconds

• 1 second and 4 seconds

• -1 second and 4 seconds

Answer explanation

To find when the object hits the ground, set h(t) = 0: -8t^2 + 24t + 32 = 0. Using the quadratic formula, we find t = 4 seconds (the positive solution). Thus, it takes 4 seconds for the object to hit the ground.

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.B.4

A dolphin jumps from the water at at initial velocity of 16 feet per second. The equation h = -8t² + 16t models the dolphin's height at any given time, t. What is the maximum height the dolphin jumps?

• 1 foot

• 5 feet

• 7 feet

• 8 feet

• 12 feet

Answer explanation

To find the maximum height, use the vertex formula for a parabola. The maximum height occurs at t = -b/(2a) = 16/(2*8) = 1 second. Plugging t = 1 into the height equation gives h = -8(1)^2 + 16(1) = 8 feet.

Tags

CCSS.HSA.REI.B.4

CCSS.HSA.SSE.A.1

(x³-2x²+x-6)÷(x+3)

• x²-5x+16+(-54/x+3)

• x²+x+16+(-54/x+3)

• x²+x-2

• x²+5x-16+(54/x+3)

Answer explanation

To divide (x^3 - 2x^2 + x - 6) by (x + 3), use polynomial long division. The result is x^2 - 5x + 16 with a remainder of -54. Thus, the answer is x^2 - 5x + 16 + (-54/(x + 3)), matching the correct choice.

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.B.3

Which of the following could be the equation of this polynomial function?

Answer explanation

The correct choice, \( f(x) = (x+5)^2(x+1)(x-3) \), indicates a double root at \( x = -5 \) and single roots at \( x = -1 \) and \( x = 3 \). This matches the behavior of the polynomial function.

Tags

CCSS.HSA.APR.B.2

CCSS.HSA.APR.B.3

What could be the equation of this polynomial function?

Answer explanation

The correct polynomial function is given by the roots at x=4, x=-1, and x=-3. The choice f(x)=(x-4)(x+1)(x+3) accurately reflects these roots, while the other options include unnecessary multiplicities or incorrect roots.

Tags

CCSS.HSA.APR.B.2

CCSS.HSA.APR.B.3

Which of the following is the equation of the graph with vertex (1,7) and goes through the point (2,5)?

Answer explanation

The vertex form of a parabola is y=a(x-h)^2+k. Here, (h,k) is (1,7). To find 'a', use the point (2,5): 5=-2(2-1)^2+7, which simplifies to a=-2. Thus, the equation is y=-2(x-1)^2+7.

Tags

CCSS.HSA.CED.A.2

What is the increasing interval for the function below?

Answer explanation

The function is increasing on the interval where its derivative is positive. Analyzing the function, it is found to be increasing for all x values less than 2, hence the correct interval is \((-\infty, 2)\).

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

What is/are the increasing interval(s) for the function shown?

• [4, 8]

Answer explanation

The function is increasing in the interval (4, 8) as the derivative is positive in this range. The other options either include incorrect intervals or do not reflect the increasing behavior of the function.

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7