Precalc Final Exam Chunky Review - E1

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What are polynomials?

Equations with constants, variables, & exponents (non-negative integer powers, so no x^(-2) )

What is the GCF? How do you calculate it?

The Greatest Common Factor is the factor that can be shared with each term. To calculate it, look at the terms in the equation and find the highest value and factors they share.

What do you do for a polynomial with an even number of terms?

You can divide the equation into groups!

What is the difference of squares?

This just means that you are allowed to divide it into two groups, so x² - y² can become (x+y)(x-y)

When working with fractional expressions, do you use the LCD/LCD or the inverse of the fraction to simplify?

You always use LCD/LCD to simplify

What does “rationalising the square root” mean?

Getting rid of the square root (from the denominator)!

What is a function?

A function is an expression that has exactly one output for each input.

What is the domain of a function? How do you solve for domain?

The domain is the set of all possible x values. To find it, set the simplified denominator of the equation equal to 0.

What is the range of a function? How do you find it algebraically?

The set of all possible y values. To find it, look at the function’s behaviour (limits).

How do you find the domain of a cube root equation?

Cube roots by themselves are always all real numbers.

What do you NEVER do when finding domain and range?

NEVER divide by 0 and NEVER put a negative in a square root (odd numbered roots are fine)

What is a piecewise function?

A function with multiple equations that each have a certain domain.

What is the FoG domain rule?

x must be in the domain of g, and g(x) must be in the domain of f for f(g(x)).

What is the formula for transforming graphs?

f(x) = a (bx - c) + d where “a” vertically scales, “b” compresses/stretches, “c” moves left/right, and “d” moves up/down

What is vertical scaling?

Each y coordinate is multiplied by the “a” value