What is the simplified form of each rational expression? Specify the domain. 4. $$\frac{2x^2 + 11x + 5}{3x^2 + 17x + 10}$$

(2x + 1)/(3x + 2), x ≠ -5, -2

(2x + 5)/(3x + 10), x ≠ -5, -2

(2x + 1)/(3x + 2), x ≠ -2, -1

What is the simplified form of each rational expression? Specify the domain. 5. $$\frac{6x^2 + 5xy - 6y^2}{3x^2 - 5xy + 2y^2}$$

(2x + 3y)/(x - 2y), x ≠ 2y, y ≠ 0

(2x - 3y)/(x + 2y), x ≠ -2y, y ≠ 0

(3x + 2y)/(x - y), x ≠ y, y ≠ 0

(2x + y)/(x - 3y), x ≠ 3y, y ≠ 0

Find the product and the domain. 9. ((5y - 20) / (3y + 15)) · ((7y + 35) / (10y + 40))

(y - 4)/(2y + 8), y ≠ -5, -2, -4

(y + 4)/(2y - 8), y ≠ 5, 2, 4

(y - 4)/(2y - 8), y ≠ 5, 2, 4

(y + 4)/(2y + 8), y ≠ -5, -2, -4

Find the quotient: 11. $$\frac{y^2 - 49}{(y - 7)^2}$$ ÷ $$\frac{5y + 35}{y^2 - 7y}$$

(y + 7)/(y - 7), y ≠ 0, 7, -7

(y - 7)/(y + 7), y ≠ 0, 7, -7

(y + 7)/(y + 7), y ≠ 0, 7, -7

$$\frac{y^2 - 49}{5y + 35}$$ , y ≠ 0, 7, -7

Find the quotient: 12. $$\frac{y^2 - 5y + 4}{y^2 - 1}$$ ÷ $$\frac{y^2 - 9}{y^2 + 5y + 4}$$

$$(y^2 - 5y + 4)(y^2 + 5y + 4)/((y^2 - 1)(y^2 - 9))$$ , y ≠ 1, -1, 3, -3, -4

$$(y^2 - 9)(y^2 - 1)/((y^2 - 5y + 4)(y^2 + 5y + 4))$$ , y ≠ 1, -1, 3, -3, -4

$$\frac{y^2 - 5y + 4}{y^2 - 9}$$ , y ≠ 3, -3, 4, -4

$$\frac{y^2 + 5y + 4}{y^2 - 1}$$ , y ≠ 1, -1, -4

Find the sum: 13. $$\frac{6y^4}{y^2 - 5}$$ + $$\frac{3y + 1}{y^2 - 5}$$

$$(6y^4 + 3y + 1)/(y^2 - 5)$$ , y ≠ √5, -√5

$$(6y^4 + 3y - 1)/(y^2 - 5)$$ , y ≠ √5, -√5

$$\frac{6y^4 - 3y + 1}{y^2 - 5}$$ , y ≠ $$\sqrt{5}$$ , - $$\sqrt{5}$$

$$(6y^4 + 3y + 1)/(y^2 + 5)$$ , y ≠ √5, -√5

Find the sum: 14. $$\frac{(x + 2)}{(x^2 + 4x + 4)}$$ + $$\frac{2}{(x + 2)}$$

$$\frac{x^2 + 4}{x + 2}$$ , x ≠ -2

$$\frac{x + 2}{x^2 + 4}$$ , x ≠ -2

Find the sum: 15. $$\frac{4}{x^2 - 25}$$ + $$\frac{6}{x^2 + 6x + 5}$$

$$\frac{4x^2 + 24x + 44}{x^2 - 25}(x^2 + 6x + 5)$$ , x ≠ 5, -5, -1, -5

$$(4x^2 + 6x + 5)/(x^2 - 25)(x^2 + 6x + 5)$$ , x ≠ 5, -5, -1, -5

$$(10x^2 + 30x + 50)/(x^2 - 25)(x^2 + 6x + 5)$$ , x ≠ 5, -5, -1, -5

$$\frac{4x^2 + 24x + 40}{x^2 - 25}(x^2 + 6x + 5)$$ , x ≠ 5, -5, -1, -5

Solve the equation: $$\frac{1}{2x-3} = \frac{1}{5-2x}$$ Write your answer in simplest form.

No solution (the denominators are negatives of each other, so the equation is never true).

Solve the equation: $$2 - \frac{1}{x+3} = \frac{1}{x+3}$$ Write your answer in simplest form.

x = -3 (but this makes the denominators zero, so no solution)

Find the inverse of the function f(x) = $$x^2 + 10x + 25$$ . Identify an appropriate restriction of its domain.

Inverse: f(x) = $$(x+5)^2$$ , so y = $$(x+5)^2$$ → x = $$(y+5)^2$$ → y = $$\sqrt{x}$$ - 5 (restrict domain to x ≥ -5)

Inverse: f(x) = $$(x-5)^2$$ , so y = $$(x-5)^2$$ → x = $$(y-5)^2$$ → y = $$\sqrt{x}$$ + 5 (restrict domain to x ≥ 5)

Inverse: f(x) = $$x^2 + 10x + 25$$ , so y = $$x^2 + 10x + 25$$ → x = $$y^2 + 10y + 25$$ (restrict domain to x ≥ 0)

Inverse: f(x) = $$(x+5)^2$$ , so y = $$(x+5)^2$$ → x = $$(y+5)^2$$ → y = $$\sqrt{x}$$ + 5 (restrict domain to x ≥ -5)

Use composition to determine whether f and g are inverse functions. f(x) = (1/5)x - 3, g(x) = 5x + 15

Yes, f(g(x)) = (1/5)(5x+15) - 3 = x + 3 - 3 = x; g(f(x)) = 5((1/5)x - 3) + 15 = x - 15 + 15 = x. So, they are inverses.

No, f(g(x)) = (1/5)(5x+15) - 3 = x + 3 - 3 = x; but g(f(x)) = 5((1/5)x - 3) + 15 = x - 15 + 15 = 2x, so they are not inverses.

No, f(g(x)) = (1/5)(5x+15) - 3 = x + 3 - 3 = 2x; g(f(x)) = 5((1/5)x - 3) + 15 = x - 15 + 15 = x, so they are not inverses.

No, f(g(x)) = (1/5)(5x+15) - 3 = x + 3 - 3 = x; g(f(x)) = 5((1/5)x - 3) + 15 = x - 15 + 15 = 0, so they are not inverses.

Find f⁻¹(x) for the function f(x) = (4 - (9x)²)/3.

f⁻¹(x) = (sqrt(4 - 3x))/9 and f⁻¹(x) = -(sqrt(4 - 3x))/9

f⁻¹(x) = (sqrt(3x - 4))/9 and f⁻¹(x) = -(sqrt(3x - 4))/9

f⁻¹(x) = (sqrt(4 - 9x))/3 and f⁻¹(x) = -(sqrt(4 - 9x))/3

f⁻¹(x) = (sqrt(9x - 4))/3 and f⁻¹(x) = -(sqrt(9x - 4))/3

Algebra 2 Honors Final Review 2025 Day 3-5

11th Grade

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88 Qs

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Algebra 2 Honors Final Review 2025 Day 3-5

Quiz

•

Mathematics

•

11th Grade

•

Practice Problem

•

Hard

Gail Sylvester Conrad

FREE Resource

88 questions

Show all answers

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

When the sun shines at a 60° angle to the ground, Talisa’s shadow is 36 in. long. To the nearest inch, how tall is Talisa?

21 inches

18 inches

31 inches

42 inches

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is another way to represent an angle in standard position that has a measure of 530°?

370°

170°

10°

-10°

-170°

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

A car is on a Ferris wheel with a radius of 20 feet. To the nearest foot, how far does the car travel over an angle of π/3 radians?

21 feet

12 feet

35 feet

42 feet

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

(a) x = log(8)/log(3); (b) x ≈ 1.893

(a) x = log(3)/log(8); (b) x ≈ 0.530

(a) x = log(8)/log(2); (b) x ≈ 3.000

(a) x = log(2)/log(3); (b) x ≈ 0.631

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the solution to the equation log₃(2x - 3) = -1?

x = 1

x = 0

x = 2

x = -1

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

(a) x = log(8)/log(3); (b) x ≈ 1.893

(a) x = log(3)/log(8); (b) x ≈ 0.530

(a) x = log(8)/log(2); (b) x ≈ 3.000

(a) x = log(2)/log(3); (b) x ≈ 0.631

FILL IN THE BLANK QUESTION

30 sec • 1 pt

Solve the equation 8^(x+1) = 2^(x-5) by using a common base.

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Algebra 2 Honors Final Review 2025 Day 3-5

88 questions

When the sun shines at a 60° angle to the ground, Talisa’s shadow is 36 in. long. To the nearest inch, how tall is Talisa?

What is another way to represent an angle in standard position that has a measure of 530°?

A car is on a Ferris wheel with a radius of 20 feet. To the nearest foot, how far does the car travel over an angle of π/3 radians?

What is the solution to the equation log₃(2x - 3) = -1?

Solve the equation 8^(x+1) = 2^(x-5) by using a common base.

Multiply and divide rational expressions. Simplify: 1. (4x + 6) / (2x + 3)

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