Answers 25-26 TX-Algebra II CRCumulative Exam

Cumulative Exam — Cumulative exam Answers

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The quadratic model f(x) = –5x2 + 200 represents the approximate height, in meters, of a ball x seconds after being dropped. The ball is 50 meters from the ground after about how many seconds?

2.45

3.16

5.48

7.07

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The amount of a sample remaining after t days is given by the equation , where A is the initial amount of the sample and h is the half-life, in days, of the substance. A sample contains 18% of its original amount of Radon-222. The half-life of Radon-222 is about 3.8 days. Which is the best estimate for the age of the sample?

1.5 days

2.5 days

9.4 days

21.1 days

The parent function f(x) = x3 is translated to form g(x), as shown on the graph. The translated function can be written in the form g(x) = (x – h)3 + k.

h = 4 k = –2

h = –4 k = –2

h = 4 k = 2

h = –4 k = 2

Which expression is equivalent to the following complex fraction?

StartFraction (y + 1) (y minus 1) Over y squared EndFraction

StartFraction y + 1 Over y minus 1 EndFraction

StartFraction y minus 1 Over y + 1 EndFraction

StartFraction y squared Over (y + 1) (y minus 1) EndFraction

How does the graph of g(x) = 3x – 2 compare to the graph of f(x) = 3x?

The graph of g(x) is a translation of f(x) 2 units left.

The graph of g(x) is a translation of f(x) 2 units right.

The graph of g(x) is a translation of f(x) 2 units up.

The graph of g(x) is a translation of f(x) 2 units down.

The graph below shows the function .Which statement is true?

There is a hole at x = 3 and an asymptote at x = –1.

There is an asymptote at x = –1 and no hole.

There is a hole at x = 3 and no asymptote.

There is an asymptote at x = 3 and a hole at x = –1.

What is the domain of the square root function graphed below?

x greater-than-or-equal-to negative 4

x greater-than negative 4

x greater-than-or-equal-to 0

x greater-than 0

What is the solution of ?

x = –2500

x = –50

x = –2.5

no solution

For what value of x does ?

no solution

Determine if the given function has any points of discontinuity. Explain your reasoning.

There is a point of discontinuity at x = b because the denominator has the factor x – b.

There are points of discontinuity at both x = – b and x = b because the numerator has factors of x + b and x – b.

There is a point of discontinuity at x = -b only because the factor of x – b is common to both the numerator and denominator.

There is a point of discontinuity at x = b only because the factor of x – b is common to both the numerator and denominator and factors out.

Which of the following is the inverse of ?

y = log Subscript one-twelfth Baseline x

y = log Subscript 12 Baseline StartFraction 1 Over x EndFraction

y = log Subscript x Baseline 12

y = log Subscript 12 Baseline x

Myra uses an inverse variation function to model the data for the ordered pairs below.(2, 30), (3, 20), (4, 15), (5, 12), (6, 10)Which statement best explains whether an inverse variation function is the best model for the data?

An inverse function is the best model because as x increases, y decreases.

An inverse function is the best model because the products of corresponding x- and y-values are equal.

An inverse variation function is not the best model because data points approximate a straight line.

An inverse variation function is not the best model because the data points show an exponential decay.

Which equation describes a rational function with x-intercepts at –4 and 2, a vertical asymptote at x = 1 and x = –1, and a horizontal asymptote at y = –3?

f(x) =

The data in the table represent the height of an object over time.

quadratic, because the height of the object increases or decreases with a multiplicative rate of change

quadratic, because the height increases and then decreases

exponential, because the height of the object increases or decreases with a multiplicative rate of change

exponential, because the height increases and then decreases

Phan fills the tank of her car with gasoline before starting her road trip. The table below shows the amount of gas left in her tank as she drives.Number of Hours vs. Amount Left in TankNumber of Hours Spent Driving (h)3579Amount of Gas Left in Tank, in gallons (g)12840Which equation models the amount of gas left in the car as Phan drives, and how many gallons of gasoline does it take to fill her tank?

g = 18 – 2h; 18 gallons

g = 18 – 2h; 16 gallons

g = 3h + 3; 30 gallons

g = 3h + 3; 12 gallons

The graph of a logarithmic function is shown below.What is the domain of the function?