End of Semester Test: Algebra 2A - Plato

Consider the function f(x) = x^2 -3x / x^2 -9

A.)

Use synthetic division to find all the factors of this polynomial. 4x^3 + 5x^2 - 18x + 9

(x - 1)(4x - 3)(x + 3)

Jesse is traveling up and down a stream in a kayak. He can paddle the kayak at an average rate of 5 miles/hour, and the round trip is a total distance of 16 miles. When c is the speed of the current, this expression can be used to find the difference of the time it takes Jesse to travel upstream (against the current) and downstream ( with the current). 8/5-c minus 8/5 +c

16c/25-c^2

Using long division, what is the quotient of 3x^4 + 20x^3 + 14x^2 + 17x +30 and x + 6?

D.) 3x^3 + 2x^2 + 2x + 5

What is the domain of this radical function? f(x) = (√x + 1) - 3

D.) [-1, ∞)

Which of the given functions could this graph represent?

D.) f(x) = (x - 1)(x - 2)(x +1)(x + 2)

If no denominator equals zero, which expression is equivalent to (x + 2)/ x^2 - 16 divided by (2x + 4)/x^2 + 3x - 4

x -1 / 2(x - 4)

It would take Charlene and Gina 18 minutes to organize Charlene's comic book collection if they work together. If Gina works alone, it would take her 15 minutes longer than it would take Charlene working alone. When x represents the number of minutes it takes Charlene to organize the comic book collection working alone, the situation is represented by this equation: 1/x + 1/x + 15 = 1/18 Which value is a solution of the rational equation that must be discarded because of the context?

x = -9

Use the drawing tools to from the correct answers on the graph. Complete the function table for the given domain, and plot the points on the graph.

(2,10), (3,5), (4,2), (5,1), (6,2)

What are the zeros of the function y = (x -4)(x^2 - 12x + 36)

B.) 4 and 6

Which expression is equivalent to 32 cube root 18y / 8 cube root 3y

B.) 4 cube root 6

What is this expression in simplest form? 4w/w - 2 + 3w/w - 3

B.) 7w^2 - 18w / w^2 -5w + 6

Which of these is a non-real complex number?

B.) 8/3 + √-7/3

What is the solution to the equation? √x + 6 = x

B.) 9

The graph of function f is shown. which statement correctly describes the graph of g(x) = f(x-9)

B.) Function g has the same horizontal asymptote as f and a vertical asymptote of x = 6

Which statement about the zeros of the graphed function is true?

B.) The function has two distinct real zeros and two complex zeros. (This is incorrect)

Which function displays this end behavior? As x approaches negative infinity, y approaches positive infinity As x approaches positive infinity, y approaches negative infinity

B.) y = -2x^3 - 1

Consider these functions. f(x) = -2x -5 g(x) = x - 2 Which graph shows the composite function (f × g)(x)

C.)

Which expression is equivalent to this polynomial?

C.) (x + 2√3)^2 (This is incorrect)

Consider these functions. f(x) = -1/2x^2 + 5x g(x) = x^2 + 2 What is the value of f(g(-2))

C.) 12

What is the solution to the equation? cube root 2x + 5 = 5

C.) 60

What is the completely factored form of this polynomial? 7x^4 + 14x^3 - 168x^2

C.) 7x^2(x - 4)(x + 6)

Which statement describes the solutions of this equation? 4/3x + 1 = x/2x + 10

C.) The equation has two valid solutions and no extraneous solutions.

The parent function f(x) = cube root x is transformed to g(x) -2f(x). Which is the graph of g?

D.)

Cassie's age is 3 less than twice Kara's age. The sum of their ages is 42. Create an equation to find Kara's age, n.

n + (2n - 3) = 42

Each ticket for an art museum costs $12.50. The total cost for student tickets, t, varies directly as the number of tickers, s, purchased. Write an equation that models the proportional relationship between t and s.

t = 12.5s

Consider function f. f(x) = cube root -x - 1

D.) Z

Which expression is equivalent to the given polynomial expression? (9v^4 + 2) + v^2(v^2 w^2 + 2w^3 - 2v^2) - (-13v^2 w^3 + 7v^4)

D.) v^4 w^2 + 15v^2 w^3 + 2

The values x = 2 ± i are the roots of the quadratic equation

x^2 - 4x + 5 =0

A company's monthly profit, y, in relation to the number of salespeople employed, x, is shown on the graph. Based on the quadratic model, approximately what number of salespeople maximizes the company's profits?

D.) 37

Rewrite the expression 2 fourth root x^7 using rational exponents

2x^7/4

Simplify the following expression into the form a + bi, where a and b are rational numbers.

9 - 25i

Use the properties of exponents to rewrite this expression. (2a^4)^2/a^0a^5 What is the value of the rewritten expression when a = -5?

A.) -500

Which expression in factored from is equivalent to this expression? 4(x^2 - 2x) -2(x^2 - 3)

A.) 2(x - 1)(x - 3)

Sarah owns a flower shop and can model the profits from selling springtime bouquets using this equation, where b is the number of springtime bouquets. P = -5b^2 + 450b - 1,000 Which statement is true if Sarah needs to make a profit of at least $9,000?

A.) Sarah must sell between 40 and 50 springtime bouquets.

What are the x- and y-intercepts of the function g(x) = (x + 1)(x^2 - 10x +24)

A.) x-intercepts: -1, 4, 6; y-intercept: 24

What is the factored form of this expression? x^9 - 1,000

B.) (x^3 - 10)(x^6 + 10x^3 + 100)

What is the simplest form of the expression 2x(x - 6) -7x^2 -(13x-3)

B.) -5x^2 - 25x + 3

The amount of force, F, needed to life an object using a lever varies inversely as the length, l, of the lever. When a 24-inch lever is used, a force of 240 pounds is needed. How much force is needed if a 36-inch long lever is used?

B.) 160 pounds

Maggie is training for a bicycle trip across her home state. She recorded the approximate number of miles she biked during 10 days of training. The graph shows the data that she recorded as a function of the distance biked over time. Which function best models the data set?

D.) y = 10/3x + 8

Function g is a transformation of the parent exponential function. Which statements are true about function g?

Function g has a y-intercept of (0,4) Function g is positive over the interval (-∞,∞) The range of function g is (3, ∞)

Max used these steps to find the inverse of function f. Use this information to complete the statement.

Max made a mistake in step 5, he should have used division instead of multiplication.

Which function is the inverse of f(x) = (√x -2)/6

f^-1(x) = 36x^2 + 2, for x is greater than or equal to 0

What is the simplest form of the expression representing this product. (x + 10)/x^2 + 7x - 18 times 3x^2 - 12x + 12 / 3x + 30

x - 2 / x + 9