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Terms in this set (64)
the identity function
f(x)=x
the squaring function
f(x)=x²
The cubing function
f(x)=x³
the reciprocal function
f(x)=(1/x)
the square root function
f(x)=√x
the exponential function
f(x)=eⁿ
the natural logarithm function
f(x)=ln x
the greatest integer function
f(x)=int (x)
the absolute value function
f(x)=abs(x)
the sine function
f(x)=sin x
the basic logistc function
f(x)=(1)/(1+e⁻ⁿ)
the cosine function
f(x)=cos(x)
f(x)=x
f(x)=x²
f(x)=b^x, when b>1
f(x)=|x|
f(x)=x³
ƒ(x)=√x
ƒ(x)=1/x
positive numbers
The numbers to the right of 0 on the number line.
negative numbers
The numbers to the left of 0 on the number line.
integers
The numbers...-3, -2, -2, 0, 1, 2, 3.....
absolute value
The distance between 0 and a number on the number line.
opposites
Numbers with the same absolute value on opposite sides of 0 on the number line; -3 and 3 are opposite.
expression
A number, or a group of numbers with operation signs
simplify
Perform the operations; find the value
base
a factor; in 3², 3 is the base used as a factor 2 times
exponent
the number that tells how many times the base is used as the factor
power
the product when factors are the same; in 3²=9, 9 is the power
Order of Operations
rules that tell which operation to do first
variable
a letter that represents a number
terms
parts of an expression separated by a + or a - sign
constants
numbers, or qualities, that do not change
coefficient
a number that multiplies a variable
like terms
terms that have the same variables with the same exponents
substitute
replacing a variable with a number or difference
equation
a statement that two expressions are equal
commutative property
the order of two numbers doesn't matter when you add or multiply
associative property
the grouping of more than two numbers does not matter when you add or multiply
slope intercept form
point slope form
where m is the slope and (x1, y1) is a point on the line
This is another format for straight line equations. Use when you know a point and the slope; it helps find the y-intercept
y - intercept
the y-coordinate of the point where the line crosses the y-axis
How to Write a Linear Function
Ex: Write an equation for the linear function ƒ with the values ƒ(0) = 5 and ƒ(4) = 17.
1 - Write ƒ(0) = 5 as (0, 5) and ƒ(4) = 17 as (4, 17)
2 - Calculate the slope using the formula
3 - The y-intercept is 5 because the line crosses at (0,5)
Write in slope intercept form: y = mx + b
How to Write an Equation of a Line in Slope-Intercept Form
1 - Identify the slope m. You can use the slope formula if you know two points on the line.
2 - Find the y-intercept. You can substitute the slope and the coordinates (x, y) of a point on the line in y = mx + b. Then solve for b.
3 - Write an equation using y = mx + b
Standard Form
can be used to find the x- and y-intercepts.
Ax + By = C
A, B, C are integers (no fractions or decimals)
A should be positive
Slope Formula
What do you need to graph a line?
the slope and the y-intercept
Write the equation of a line that passes through the point with the given slope
plug the slope and a point into y = mx + b
solve for b
Write the equation
Write the equation of a line in slope intercept form that passes through two points
use the formula to find the slope
plug the slope and a point into y = mx + b
solve for b
Write the equation
converse
the statement formed by exchanging the hypothesis and conclusion of a conditional statement (the opposite)
Parallel Lines
If two nonvertical lines in the same plane have the same slope, then they are parallel.
If two nonvertical lines in the same plane are parallel, then they have the same slope.
To Write an Equation of a Parallel Line:
Write an equation of the line that passes through (-3, -5) and is parallel to the line y = 3x - 1
1 - Identify the slope (in this case = 3)
2 - Use the slope and the point to solve for b in y = mx + b
3 - Write the equation using y = mx + b
Perpendicular Lines
If two nonvertical lines in the same plane have slopes that are negative reciprocals, then the lines are perpendicular.
If two nonvertical lines in the same plane are perpendicular, then their slopes are negative reciprocals.
To determine whether lines are parallel or perpendicular
write all equations in slope-intercept form ( y = mx + b)
compare their m value: if the same, then parallel; if negative reciprocals, then perpendicular
Scatter Plot
is a graph used to determine whether there is a relationship between paired data. Scatter plots can show trends in data.
Positive Correlation
y tends to increase, as x increases
Negative Correlation
y tends to decrease, as x increases
Relatively No Correlation
x and y have no apparent relationship
Line of Best Fit
The line that most closely follows a trend in data is called the best-fitting line.
Linear Regression
the process of finding the best-fitting line to model a set of data; you can use technology to do this
Linear Interpolation
using a line or its equation to approximate a value between two known values
Interpolate Using an Equation
1 - Make a scatter plot of the data
2 - Graph the best fitting line
Linear Extrapolation
using a line or its equation to approximate a value outside the range of known values
Zeros of a Function
for the function ƒ, any number x such that ƒ(x) = 0
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Verified questions
ALGEBRA
Each day, an average adult moose can process about 32 kilograms of terrestrial vegetation (twigs and leaves) and aquatic vegetation. From this food, it needs to obtain about 1.9 grams of sodium and 11,000 calories of energy. Aquatic vegetation has about 0.15 gram of sodium per kilogram and about 193 calories of energy per kilogram, whereas terrestrial vegetation has minimal sodium and about four times as much energy as aquatic vegetation. Write and graph a system of inequalities that describes the amounts t and a of terrestrial and aquatic vegetation, respectively, for the daily diet of an average adult moose.
ALGEBRA2
The logistic growth function $$ f ( t ) = \frac { 100,000 } { 1 + 5000 e ^ { - i } } $$ describes the number of people, f(t), who have become ill with influenza t weeks after its initial outbreak in a particular community. How many people were ill by the end of the fourth week?
ALGEBRA
The volume V (in cubic feet) of an aquarium is modeled by the polynomial function $$ V ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 13 x + 10 $$ where x is the length of the tank. a. Explain how you know x = 4 is not a possible rational zero. b. Show that x - 1 is a factor of V(x). Then factor V(x) completely. c. Find the dimensions of the aquarium shown.
PRECALCULUS
Points A and B are 257 nautical miles apart. How far apart are A and B in statute miles?