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WorksheetsUnit 1: Linear, Polynomial, and Rational Functions Vocab
Total questions: 88
Worksheet time: 50mins
Stand and Fight
Yes
No
Is it true that the slope is the rate of change of any two points?
True
False
When looking at two coordinates, you shouldn't decide to call the x and y of the same coordinate by the same letter to identify them, but different numbers.
False. You want to name each x and y of each coordinate the same number
True it make sense to every each letter with different number
Which of the following equation isn't equal to the slope
m = slope
Δy⁄Δx = m
(Y2 - Y1)/(X2-X1)
(Y1-Y2)/(X1-X2)
b = y - intercept
My friend Dennis kept talking about how slope is rising over run. I was curious, is it left to right or right to left
Right to left
Left to Right
What is the definition of reciprocal
a mathematical expression or function so related to another that their product is one; the quantity obtained by dividing the number one by a given quantity.
the rise and run just switch!
x and y switch sides amigos
blah blah blah switch
What is a Linear Function?
y = mx + b
slope
constant
a slope greater than 0
A Linear equation has a constant change
Yes
No
What are some synonyms for constant in Linear Equation
Same
Consistent
Slope
Y-intercept
What is slope intercept form
y = mx + b
ax+by = c
What is the standard form for math
Ax + By = C
y = mx + b
Two negatives make a
positive
negative
How many points do you need to graph a line?
2
1
3
5
When trying to find the points for the linear function, is it true your y intercept from your slope form is enough?
Yes, just make sure to find the rest
Plug in 0 for x because the y-intercept is written as (0,y), where the x-intercept must be zero
Plug in 0 for the x because the y-intecept is written as (y,0), where the y-intercept must be zero
When given a slope equation of graph you generally have to options to graph and find the equation.
Plug in x-values
Find it in the graph
Oh no! You fell for the standard forms traps, now you don't know how to graph it. Wait, what can you recall about it....
Linear functions are written as y = mx + b, some maybe isolate the y by doing the opposite on both sides.
We want to make sure that the variable with a letter goes In front of the constant.
You must divide each variable if there is a need to do the opposite which is division
Make sure to put the negative and variable In-front of the constant
Yes
No
Its true that sometimes you just want to go through and guess the y-intercept, but equations are much more accurate
Yes
No
What are the two special lines
horizontal line
vertical line
What is the vertical equation
its vertical, doy
its x =
its horizontal
its y =
What is the horizontal equation
x =
horizontal equation
Oh darn, you are given just coordinates to solve a problem. No worries! Use the slope formula to use the two points and find the slope
OKAY!!
Sounds to hard!!!
When given the juicy yummy slope. Just get on of the coordinates, plug in the x and y value into the slope formula, and solve for b!
Yup
Okay!
two lines in the same plane that are at equal distance from each other
parallel lines
perpendicular lines
Perpendicular lines are lines that intersect at a 90 degrees angle
True
False
What are the characteristics of a parallel line
Two lines never intercept
The two lines intercept a 90 degree angle
the slopes are the same
the slopes are reciprocal
What are characteristics of a perpendicular line
It intercepts a 90 degree angle
the slope is the the reverse of the other
the slope changes sign
the slope stays the same
When answering a equation following with the idea of slopes from coordinates and stuff, make sure to focus on if it asks for parallel or perpendicular
Of course!
No, ingore It mwahahahahah
Check your answers if you can!
Yup
Of course
What is a relation in functions
A relation is a correspondence between two sets of pairs from two sets together
A relation of a whole set being the same number
A set of inputs
Domain
Range
Output
Range
Domain
What is a function
a special relation
every x gets its own y
a y can have multiple x's but an x cant have multiple y
What is the vertical line test
X = a
Vertical Line
Determine if a function is a function
Tewkmpinovdhnidqklhcnbsifubwsdjfebchbehyufb
the -----r numbers are all the real numbers that are not rational numbers.
rational
irrational
a number that is expressed as the ratio of two integers, where the denominator should not be equal to zero
irrational
rational
integers
a number that is not a fraction; a whole number.
irrational
integers
rational
What ways can you express domain and range
Smallest to Biggest
Interval Notation
Inequality
Verbal Statement
Rational
What causes undefined Square Root
Rationals
Fraction
Square Root
Quadratics
Linear
What does ( represent in interval notation
Infinite
Finite
Finite?
]
)
Is it true that rationals can not be negative numbers but positive numbers
True
False
When finding the domain of a rational, make the rational greater than 0 as 0 is above negative numbers. When dividing and multiplying on both sides, what happens when the number dividing or multiplying is negative?
Flip the greater than and equal
Flip the greater than sign
Flip the less than and equal sign
How do you find domain square root you gotta
x≥0
x≤0
Rationals are just Fractions, and fractions don't like be divided by zero. So what can we do to the factors below the numerator to find what x equals as 0
Make the factors below equal to 0 and solve for x
Make the factors above equal to 0 and solve for x
Adding - Operations on Functions
(f+g)(x) = f(x) + g(x)
(f-g)(x) = f(x) - g(x)
fg(x) = f(x)g(x)
f/g(x)=f(x)/g(x)
Subtracting Operations
(f-g)(x)
f/g(x)
Multiplying Operations
fg(x)
f/g(x)
Dividing factors
f/g(x)
fg(x)
We can operate on function to create new functions or to evaluate as if we would with number
Operations on Functions
Operations on Cats
Its possible to plug in a value in one equation, and plug the result into another equation. Just make sure to write that result into the x part of f(x) not the result into the original like (h(0) in what was h(2) (Say cookie if you read
Yes
No
Cookie
When finding results from f(0), its the y value we are finding with the x-value
Yes
No
If the line is going up and given and x value to determine if positive or negative, you say
positive
negative
If the line is going down and given and x value to determine if positive or negative, you say
negative
positive
When given values where x values f(x) = 0, its just the x-intercept
Yes
No
domain is up and range is side
wrong
true!!!
When given a function that is not continuous, you want to make sure that your start left to Right.
Yes
No
If the value say f(x) > 0, make sure to make an interval notaion min to max where its [x,x) (x,4} where it demonstrates continuity but it cancels out at a certain point
Yes
No
When you are given a fuaction and told to find the interval between f(x)<0, find the x values below that make it less than 0.
Yes
No
When trying to intercept a line to another, just draw the line, yo!
Of course!
Yes sir!
A function is even if it symmetrical across the
y-axis
origin
x-axis
A function is odd when it reflects accros
the origin
the y-axis
non-default
(x,y) switched the -x to negative in what type of function
odd
even
A function that is odd would go from (x,y) to
(-x,y)
(-x,-y)
You can move a function up and down and be even, but going left and right is likely going to lead to neither and not odd.
True
False
With polynomials, you can find if a function is even by just the highest power, but what can we do with functions that are not polynomials
Still use the degree
Plug in -x to the equations
Plug in x to the equations
When plugging in the equation with -x and getting the same its a ---- function
even
odd
neither
When plugging in the equation with -x and getting opposite signs its a ---- function
odd
even
neither
When plugging in the equation with -x and getting nothing alike its a ---- function
neither function
even
odd function
More than one atom together via a covalent bond
Molecule
Dyhdration
two pieces that stick together
dehydration
hydrolysis
when to piece split off by water
Hydrolsis
Dehydration
When finding what equation to plug inside with your x value, remember to look at the the inequalities to see that fit it
Yes
No
Inequalities are different for every function of course, but what a great than or equal or a less than equal to, that number can also work
Of course. Inequalities that have an equal symbol can equal even if its greater or lower
No, inequalities always have to be greater or less than and no equal sign
What isn't an example of a constant function
x = 3
y= 2x
y = 2
y = 3x
When given ≤ what direction will be available to be true
left side
right side
When given the ≥ what direction do you look
right
left
Graphing is a simple task, but those small details always make a count, right
Yes
False
Of course they count silly!
What symbol makes an open hole
<>
≤≥
A piecewise function is just a function which is made up of ------- functions
multiple
little
Quadratic function are functions that can be written in form
f(x) = ax^2 + bx + c
y = mx
What are the key characteristics of a Quadratic Function
Concavity
Vertex
Axis of Sym
X-intercept
Y-intercept
Graphing Quadratic Function with Vertex form
a(x+h)^2+k
a(x+h)(x+k)=f(x)
What variables are found in vertex form
a
h
k
b
j
What is standard form
x^2+bx+c
a(x+h)^2+k
h = -b/2a
The h gives you part of your vertex and axis of sym
h is able to give you the a value from plugging in
plugging in h gives you the k values
When your a, b, and c values aren't integers, you could try factoring, but what would be more effective?
using the quadratic formula
using the linear equation
What is the Quadratic Formula
An easy way to find factors of a polynomial in the 2nd degree, potentially giving you imaginary numbers!
A horrible way to factor out a polynomial, make a guess!
