Algebra 2 regents prep

Use TI 84 calc. Knowadgle of general algebra 2 and an advanced calculator is required. Graph paper required. Note: do not use multiple choice

Describe the translations (movements) that map “f(x)= log x” onto “g(x)= log(x+3)-5”.

3 units to the left and 5 units down (-3,-5)

Solve algebraically for x:

x= -3

Given a > 1, use the properties of rational exponents to determine the value of x for the equation below.

x=0.5 or x=1/2

Is the mean weight of the grocery store’s sample unusual? Explain using the results of the simulation.

Yes, ________

When determining the probability for two events happening at the same time (Event A and event B) do you add or multiply the probabilities?

multiply. EX:

When determining the probability for ether two events to happen (Event A or event B) do you add or multiply the probabilities? Then what do you do?

add, then subtract by the the multiplied probabilities. EX:

Determine the exact probability that a randomly selected guest room has a view of the lake and a queen-size bed.

17.76%

Determine the exact probability that a randomly selected guest room has a view of the lake or a queen-size bed.

80.24%

how can you represent 1.333333333….

as 1x1/3

Which function has a greater average rate of change on the interval [-1,4]?

p(x)

Determine an equation for the parabola with focus (-2,4) and directrix y = 10.

y= - 1/12 (x+2)²+7

A(t)=10,000e^.25t B(t)=6000e^.45t

Use calc, graph paper and table option. Column is in intervals of 10 up to 50 (by thousands), bottom is in months 0-4. Make own line graph (search up for reference .)

State, to the nearest tenth of a month, when the colonies will have the same population.

2.6 months

Using graph paper,

graph y=3.2(1.8)^x

x+3 is a factor

Factor completely

x(2ײ+3)(x-5)

Hint: use calulator

Answer: 3 feet. Explanation:______

Hint: replace x

India had the greater rate of change. Explanation:____

What is an even function?

A function that is perfectly symmetrical through the middle:

No it is not. It is unsymmetrical

Write an equation for g(x), the function that results after f(x) is shifted up 5 units.

f(x)+5=g(x)

Given x is a real number, write the expression in simplest a + bi form:

7x+6i

Hint: once you have e and the exponent multiply e with ln so you can bring down the exponent as a real number, than just solve for t. Use like terms

t=0.96

In an attempt to get the student body’s opinion of a new dress code, members of the statistics class surveyed the students of the first period computer science class. Explain a statistical bias in the method of data collection.

Basically say how they need to investigate different classes because one class/period wouldn’t represent the student body as a whole and state your reason. Some form of that.

HInt: since p(x) is negative infinity there has to be arrows pointing downwards. Use graph paper.

It could work no matter if the “bumps” where up or down, just if they only hit those three points then went down.

What is the period of a function?

How long (horizontally: x) a function’s graph takes to complete one cycle.

Hint input into calculator and check graph/table.

Periods are the the distance between cycles (basically the maximum points) of functions. Distance between cycles in the x column was 5, meaning that is the period. The period in this context is how long the Ferris wheel takes to complete on cycle.

Whatever you multiply one side by___

Multiply the other by.

Whatever you multiply the bottom by…

Multiply the top by.

x = -3, x=-1

If two events are independent than what formula needs to be used/correct?

P(Event A and event B happening at the same time) = P(Event A) x P(event B)

There is a pile of 12 marbles. There are 4 blue marbles and 2 black marbles, with the rest being red. What is the probability of randomly picking a blue marble and then a black marble?

1/18

When doing P(A and B)= P(A) x P(B) equation, what do you divide the events by?

The total amount of data on the data, or all the chances/events combined.

If P(A and B) ≠ P(A) x P(B) is it independent?

No.

If P(A and B) = P(A) x P(B) is it independent?

Yes

Are the events “being a junior” and “driving to school” independent? Using statistical evidence, justify your answer.

No they are not independent, they do not equal being a junior and driving to school.

What is an odd function?

A function that is symmetrical with respect to the origin. Basically it is still centered on the origin but is not perfectly symmetrical while mirrored like a even function.

What is an even function?

A function that is symmetrical with respect to the y-axis. Basically it is centered on the origin and is perfectly symmetrical (it looks the same on both sides.)

Can f(x)= x³+7 be classified as an odd function? Justify your answer.

You can use calculator and draw mining graph to justify your answer, but is an odd function because the function on the graph has respect to the origin, not the y-axis. It is not perfectly symmetrical when mirrored, as you would need to flip it. Some type of wording like this.

What is the asymptote?

The point where a curved line becomes straight.

What letter would you use for a vertical asymptote?

x= ____

What letter would you use for a horizontal asymptote?

y=____

To get a a log with a base like this; what would you need to do in the TI 84 calc?

MATH then scroll down to A

Factor by grouping: x³+2ײ-3x-6 (hint: factor out gcf and find a way to group them together).

(x²-3)(x+2) You combine outside terms and inside terms since their both being mutiplied.

i²=___

-1

i=___

√-1

A function must pass the ____ ___ test, meaning it there can only be one given ___ value for any y value.

Vertical line test, x or input.

If the denominator is equal to ___ its undefined, meaning it is not an function.

0

if f(x)= x-4/x+2 than what number can x NOT be equal to?

-2

what are one to one functions?

Functions that have no repeating x-values or y-values. Use the horizontal line test.

To graph inverse functions like: y= f(x), f(x)= Log₂=—— simply switch the___ and ___ values then graph.

x and y values. Tip: look for problems with curved lines like this:

Graph y= f(x), where f(x)= log₂(x-1) + 3 using graph paper. Tip: This is an inverse function.

What is an inverse function?

A function that is mirrored along y=x. To find the second function in an inverse function simply swap the x and y values of the first and graph that.

State the equation of the asymptote of f(x) Hint: f(x) is the one with log)

f(x): x=1

remember if the curved line is vertical measure the x axis and vice versa.

When f(x) is reflected over the line y = x, a new function is formed: g(x) = 2^x-3+1. State the equation of the asymptote of g(x).

y = 1. remember: since the line is infinite and horizontal you don’t measure the x axis (since that would go on forever) but the y axis, the height of it.

If the highest degree of a polynomial is an even number than the end points when graphed will point in _____ directions.

the same

If the highest degree of a polynomial is an odd number than the end points when graphed will point in _____ directions.

different

When translating a function horizontally, to translate it (ex: f(x) tothe left or right by 4) where would you put the four?

IN parenthesis with the ± symbol. Ex: f(x±4)

When translating a function vertically, to translate it (ex: f(x) down or up by 4) where would you put the four?

OUTSIDE of parenthesis with the ± symbol. Ex: f(x) ± 4

To translate a function right by 4 (EX: x²) the number has to be _____.

Negitive: (x-4)²

To translate a function left by 14 (EX: x⁴) the number has to be _____.

Positive: (x⁴+14)

To translate a function down by 8 (EX: g(x) ) the number has to be _____.

Negative: g(x) - 8

To translate a function up by 2 (EX: f(x) ) the number has to be _____.

Positive: f(x) + 2

What is the equation for translating a function horizontally? (Use f(x))

f(x±a) -a translates right, +a translates left

What is the equation for translating a function vertically ? (Use f(x))

F(x)±a. -a translates down, a translates up

How would you reflect f(x) over the y axis?

f(x) —> f(-x)

How do you reflect f(x) over the x axis?

f(x) —> -f(x)

What is an even function?

A function that is symmetrical around the y-axis

What is an odd function?

A function that has 180 degree ( means half of it was flipped) around the origin

What is the equation for Logs (ex: opposite of Log_a^c=b)

a^b=c

if Log_a^c=b then…

a^b=c

What are arithmetic sequences?

A set of numbers that are subtracted or added in order to move on to the next number.

What are geometric sequences?

A set of numbers that are multiplied or divided to move on to the next number.

If events A and B are independent than P(A) = P(A l B)