Answers CUMULATIVE EXAM MNPS English Language Arts III S1 25-26Cumulative Exam

Cumulative Exam Answers

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Which graph represents the function ?

On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens up and to the left in quadrant 2.

On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 4, and the other curve opens up and to the left in quadrants 2 and 3.

On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 2, and the other curve opens up and to the left in quadrant 3.

On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrants 3 and 4.

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The graph of y = is a horizontal translation of y = . Which is the graph of y = ?

On a coordinate plane, a cube root function goes through (negative 8, negative 2), has an inflection point at (2.5, 0), and goes through (10, 2).

On a coordinate plane, a cube root function goes through (negative 10, negative 2), has an inflection point at (negative 3, 0), and goes through (4, 2).

On a coordinate plane, a cube root function goes through (negative 10, 1), has an inflection point at (0, 3), and goes through (8, 5).

On a coordinate plane, a cube root function goes through (negative 8, negative 5), has an inflectoin point at (0, negative 3), and goes through (8, negative 1).

Which graph shows the solution set of ?

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Which of the following describes the zeroes of the graph of f(x) = –x5 + 9x4 – 18x3?

0 with multiplicity 3, –3 with multiplicity 2, and –2 with multiplicity 1

0 with multiplicity 3, 3 with multiplicity 1, and 6 with multiplicity 1

0 with multiplicity 3, 3 with multiplicity 2, and 2 with multiplicity 1

0 with multiplicity 3, –3 with multiplicity 1, and –6 with multiplicity 1

What must be a factor of the polynomial function f(x) graphed on the coordinate plane below?

x – 2

x – 1

x + 2

x + 3

If is the inverse of and , what is ?

g (x) = 12 x + 4

g (x) = one-fourth x minus 12

g (x) = x minus 3

g (x) = one-fourth x minus 3

Which graph shows the solution set of ?

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The function y = – 3 is graphed only over the domain of {x | –8 < x < 8}. What is the range of the graph?

{y | –5 < y < 5}

{y | –5 < y < –1}

{y | 1 < y < 5}

{y | 1 < y < –1}

For which interval is the average rate of change of f(x) negative?

from x = –3.5 to x = –1

from x = –3 to x = 3

from x = 0 to x = 2.5

from x = 3 to x = 4.5

Which expression is equivalent to ?

2 log Subscript 5 Baseline x + log Subscript 5 Baseline 4

2 log Subscript 5 Baseline x + log Subscript 5 Baseline 16

2 log Subscript 5 Baseline x + 2 log Subscript 5 Baseline 4

2 log Subscript 5 Baseline x + log Subscript 5 Baseline 4

The function that represents the average cost per person, including transportation, to a museum is . Which statement is true about the graph of the function?

The horizontal asymptote y = 0 means the cost approaches zero as the number of people increases.

The horizontal asymptote y = 8 means the average cost approaches $8 as the number of people increases.

The vertical asymptote x = 0 means the cost approaches zero as the number of people increases.

The vertical asymptote x = 8 means the cost approaches zero as the number of people increases.

Sabrina is tracking the growth rates of a colony of ants and of a bee hive. From her research, she has developed a function to represent the population growth of each type of insect, where y represents the population and x represents the number of weeks since Sabrina began her research. Ant Colony Growth: Bee Hive Growth: Which insect population is growing at a faster rate?

The ant colony is growing at a faster rate. It will multiply by 3.8 each week while the bee hive will add 3.8 each week.

The bee hive is growing at a faster rate. It will multiply by 3.8 each week while the ant colony will add 3.8 each week.

The ant colony is growing at a faster rate. It will add 3.8 each week while the bee hive will subtract 3.8 each week.

The bee hive is growing at a faster rate. It will add 3.8 each week while the ant colony will divide by 3.8 each week.

The table below shows the number of days, y, needed to complete a project as a function of the number of full-time staff, x, working on the project. Which rational function best models the data in the table?People Working, xDays, y36218489612

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For which pair of functions is ?

f(a) = a2 – 4 and

and g(a) = 2a – 2

f(a) = 5 + a2 and

f(a) = 3 – 3a and g(a) = 4a – 5

If f(x) = x2 – 1 and g(x) = 2x – 3, what is the domain of ?

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

x < 0

x > 0

x < 1

all real numbers

Aaliyah, Julio, Dan, and Miriam are each studying sets of data. Aaliyah is working with 14 data pairs with a correlation coefficient of 0.9. Julio is working with 13 data pairs with a correlation coefficient of –0.8. Dan is working with 10 data pairs with a correlation coefficient of 0.1. Miriam is working with 15 data pairs with a correlation coefficient of –0.2. For which two data sets is a linear regression model reasonable?

Aaliyah’s and Julio’s data sets

Julio’s and Miriam’s data sets

Dan’s and Miriam’s data sets

Miriam’s and Aaliyah’s data sets

Which graph shows the solution to the equation below?

On a coordinate plane, 2 curves intersect at (1, 1). One curve curves up and to the right from quadrant 3 into quadrant 1. The other curve curves down from quadrant 1 into quadrant 4.

On a coordinate plane, 2 identical curves are shown. One curve starts at y = negative 3, and the other curve starts at y = 1.

On a coordinate plane, a curve and a line are shown.

On a coordinate plane, a curve and a cubic function are shown.

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

What is written as a single logarithm?

log Subscript 2 Baseline left-bracket StartFraction x cubed Over (StartFraction 3 Over x + 4 EndFraction) EndFraction Right-bracket

log Subscript 2 Baseline (StartFraction 3 x cubed Over x + 4 EndFraction)

log Subscript 2 Baseline left-bracket (StartStartFraction x cubed Over 3 EndFraction) Over x + 4 EndEndFraction Right-bracket

log Subscript 2 Baseline (StartFraction x cubed Over 3 + (x + 4) EndFraction)

What is the value of ?

The graph below shows the number of houses sold over x days. What is the average rate of change from day 2 to day 10?

Negative four-thirds

Negative three-fourths

A company’s equipment manager buys $7,000 worth of equipment. This equipment depreciates 19% each year. The manager can replace the equipment after its value falls below $500.After how many years can the manager first replace the equipment?

How many liters of glycerin should be added to 12 liters of an 8% glycerin solution so that the resulting solution contains 16% glycerin? Round the answer to the nearest hundredth if necessary. Original (L)Added (L)New (L)Amount of Glycerin0.96x0.96 + xAmount of Solution12x12 + x

0.18 liter

1.14 liters

1.92 liters

2.10 liters

The polynomial function f(x) is a fourth degree polynomial. Which of the following could be the complete list of the roots of f(x)?

3, 4, 5, 6

3, 4, 5, 6i

3, 4, ,

3, 4, 5 + i, –5 + i

Which number is missing in the table of values below?xy01162363?41,296

108

216

324

648

Which phrase best describes the translation from the graph y = 2x2 to the graph of y = 2x2 + 5?

5 units up

5 units down

5 units right

5 units left

Graph the function f(x) = x3 – 3x – 2. Based on the graph, which value for x is a double root of this function?

–2

–1

If f(x) is an odd function, which statement about the graph of f(x) must be true?

It has rotational symmetry about the origin.

It has line symmetry about the line y = –x.

It has line symmetry about the y-axis.

It has line symmetry about the x-axis.

Which of the following graphs represents a function?

On a coordinate plane, a graph shows an image of a curved line connected to a straight line. The curved line is upward facing and goes through the y-axis at (0, 0.75). The curved line connects with the straight line at (1, 0.75). The straight line has a negative slope and goes through the x-axis at (2, 0).

On a coordinate plane, a circle intercepts the x-axis at points (negative 2, 0) and (2, 0) and intercepts the y-axis between points 3 and 4 and also between points negative 3 and negative 4.

On a coordinate plane, a parabola opens right and has a vertex at (negative 3, 3).

A coordinate plane has 7 points. The points are (negative 4, 3), (negative 2, negative 5), (negative 1, negative 3), (1, 3), (2, negative 2), (4, negative 2), (4, 2).

Which polynomial function has a leading coefficient of 1, roots –3 and 8 with multiplicity 1, and root 4 with multiplicity 2?

f(x) = 2(x + 3)(x + 4)(x – 3)

f(x) = 2(x – 8)(x – 4)(x + 3)

f(x) = (x + 8)(x + 4)(x + 4)(x – 3)

f(x) = (x – 8)(x – 4)(x – 4)(x + 3)

Which table shows a linear function?

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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

Which of the following gives all of the sets that contain?

the set of all irrational numbers

the set of all natural numbers, the set of all whole numbers, and the set of all integers

the set of all integers, the set of all rational numbers, and the set of all real numbers

the set of all natural numbers, the set of all whole numbers, the set of all integers, the set of all rational numbers, and the set of all real numbers

Which of the following graphs could be the graph of the function f(x) = x3 + 8?

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The height of a tennis ball tossed into the air is modeled by h(x) = 40x – 16x 2, where x is elapsed time in seconds.During what time interval will the tennis ball be at least 15 feet above the ground?

x > 0.5 seconds and x > 2.04 seconds

x > 0.5 seconds and x ≤ 2.04 seconds

x ≥ 0.5 seconds and x > 2.04 seconds

x ≥ 0.5 seconds and x ≤ 2.04 seconds

By what approximate factor is the intensity of an earthquake with magnitude 5.4 greater than an earthquake with magnitude 5.3?M = the magnitude of an earthquakeI = the intensity of an earthquakeI0 = the smallest seismic activity that can be measured, which is 1

1.01

1.21

1.26

10.44

Which graph represents the same relation as the rule y = 2x, for all real numbers x?

A coordinate plane has 5 points. The points are (negative 2, negative 4), (negative 1, negative 2), (0, 0), (1, 2), (2, 4).

On a coordinate plane, a horizontal line intercepts the y-axis at (0, 2).

On a coordinate plane, a straight line with positive slope intercepts the axis at (0, 0). The line goes through points (negative 2, negative 4) and (2, 4).

On a coordinate plane, 11 points form a vertical line that crosses the x-intercept at (2, 0).

What is the approximate value of a local maximum for the polynomial?

–4.5

–2.5

0.5

2.5

Which two functions are inverses of each other?

According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function?f(x) = (x3 – 3x + 1)2

2 roots

3 roots

6 roots

9 roots

Which graph represents the function ?

On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve down and to the left in quadrants 3 and 4.

On a coordinate plane, a hyperbola is shown. One curve opens up and to the left in quadrant 2, and the other curve opens down and to the right in quadrants 3, 4, and 1.

On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve down and to the left in quadrants 2, 1, and 4.

On a coordinate plane, a hyperbola is shown. One curve opens up and to the left in quadrant 2, and the other curve opens down and to the right in quadrants 4 and 1.

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 graph represents ?

On a coordinate plane, a parabola with a vertex at (0, 0) opens up.

On a coordinate plane, a curve that begins at (0, 0) opens down and to the right in quadrant 1.

On a coordinate plane, a cubic function is vertical and goes through (0, 0).

On a coordinate plane, a cubic function is horizontal and goes through (0, 0).

Consider the graph of f(x) = 5x 6 – 5x 5 – x 4.

One-half minus StartFraction 3 Over 10 EndFraction StartRoot 5 EndRoot less-than x less-than one-half + StartFraction 3 Over 10 EndFraction StartRoot 5 EndRoot

One-half minus StartFraction 3 Over 10 EndFraction StartRoot 5 EndRoot less-than-or-equal-to x less-than-or-equal-to one-half + StartFraction 3 Over 10 EndFraction StartRoot 5 EndRoot

x less-than one-half minus StartFraction 3 Over 10 EndFraction StartRoot 5 EndRoot and x greater-than one-half + StartFraction 3 Over 10 EndFraction StartRoot 5 EndRoot

x less-than-or-equal-to one-half minus StartFraction 3 Over 10 EndFraction StartRoot 5 EndRoot and x greater-than-or-equal-to one-half + StartFraction 3 Over 10 EndFraction StartRoot 5 EndRoot

What is the solution of ?

–8

–6

What is the value of ?

–4.00

–0.25

1.51

2.41

Juan jogs each day from his house to a local park, and then he jogs back along the same route. On his way to the park, he averages 4 miles per hour. On his way home, he averages 6 miles per hour. If the total trip takes hours, which equation can be used to find x, the distance in miles from Juan’s house to the park? Distance (mi)Rate (mi/hr)Time (hr)Trip to Parkx4 mph Trip to Homex6 mph