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Pre-calculus 12

What happens to the graph of if the equation is changed to ?

The graph of y = undergoes the transformation (x, y) . What is the resulting equation?

Determine the equation of the polynomial in factored form of the least degree that is symmetric to the y-axis, touches but does not go through the x-axis at (3, 0), and has P(0) = 27

Determine the measure of all angles that satisfy the following conditions. Give exact answers.

Solve: , over all real numbers

Use factoring to help to prove each identity for all permissible values of x. Must state restrictions over all real numbers.

In a population of moths, 78 moths increase to 1000 moths in 40 weeks. What is the doubling time for this population of moths?

Solve the following equation:

Using logarithm laws, rewrite the left side as:

Solve for x algebraically: . State your answer to the nearest hundredth.

A radioactive substance has a half-life of 92 hours. If 48g were present initially, how long will it take for the substance to decay to 3g? Show algebraically.

Given the following two functions and , evaluate .

A sample of 5 people is selected from 3 smokers and 12non-smokers. In how many ways can the 5 people be selected?

Given the functions and , determine an explicit equation for

Determine the 4th term of .

Solve by algebra

Determine the domain, range, and intercepts of . Graph the function.

For the graph of , determine an non-permissible values of , write the coordinates of any hole and write the equation of any vertical asymptote.

Sketch the graph of . State the domain, range, and equation of the horizontal asymptote.

Suppose you play a game of cards in which only 5 cards are dealt from a standard 52 deck. How many ways are there to obtain at least 3 cards of the same suit? An example of a hand that contains at least 3 cards of the same suit is 4 hearts and 1 club.

Given , determine , the inverse of .

Consider the digits 0, 2, 4, 5, 6, 8. How many 3-digit even numbers less than 700 can be formed if repetition of digits is not allowed? Note: the first digit cannot be zero.

If and , determine the value of .