Polynomial Functions
How do you tell if a relation is a function or not?
The vertical line test
When is a function "even"?
When there is an axis of symmetry through the y-axis.
What is an exponent?
A number that exist above a coefficient/solo number.
It means 3, which is the same amount of sides a triangle has!
What is domain and range?
A domain is the restrictions set on the x-value
A range is the restrictions set on the y-value
What quadrants are what positive?
1 - All
2 - Sine
3 - Tangent
4 - Cosine
What is the base equation for a rational function?
x/1
What is an exponential function?
A function that accelerates slowly, then rapidly increases to infinity.
What are the four different quadrants and is what trig identity positive in that quadrant?
Quad 1 - All
Quad 2 - Sine and Csc
Quad 3 - Tangent and Cot
Quad 4 - Cosine and Sec
What is an average rate of change?
It is a number that is determined by evaluating two intervals, shows how much a number has increased or decreased over that interval
If the leading coefficient is negative and the degree is odd, what are the end behaviours?
Both ends face upward
What are the letters used to define/signify transformations?
a, k, d, c
What is log used for?
To remove exponents to solve for "x".
What is radian measure?
Another way to identify special triangles, the unit circle, and solve equations. It includes pi
What is an instantaneous rate of change and how do you find it?
A number that is used to define how much that point increases or decreases in that exact moment, you can find this by taking a number extremely close to the given then sub that into the equation.
What are "turning points"?
What is a "hole"?
It is a specific location in the graph where the equation has crossed out a specific number from the top and bottom of the location. You then take that number, then sub it into the equation to get the y-value. Ex. when x-1 is crossed out, there is a hole at (1,?)
True or false: log functions and graphs exist
True!
How do you change degrees into radians?
Ex. 50/1 x pi/180
= 50pi/180
= simplify!
What are all the different types of functions?
Linear, exponential, rational, quadratic, and polynomial.
What is the correct format for a polynomial function?
f(x) = anx n + an−1x n−1 + . . . + a2x 2 + a1x + a0
What is specifically unique to rational functions?
They are the only type of function that (usually) has two asymptotes
Does y=log((1/9)x) have a horizontal stretch or compression?
How do you change radians into degrees?
Multiply the radian by 180/pi
Ex. 2pi/1 x 180/pi
Pi's cross eachother out
= 360
What types of functions are periodic on graphs?
Trigometric