Functions
Which of the following is a linear function?
a) y=(x+1)-4
b) y= x^2
c) y=|x+1|
d) y= sqrt of x-5
What is a) y=(x+1)-4
(A linear function is a strait line on the graph and has a parent function of y=x)
Which of these is logarithmic: Log, Tan, Sin, Cos
log
(Logarithmic functions are log x’s in graphs. They start at y=0 and gradually increase in y and x values.)
What is i^54?
-1
(i is an imaginary number for sqrt-1)
What is the LCM of 4 and 6
12
(The LCM or Least Common Multiple is the lowest number divisible by a set of numbers and is used to set up fractions to be added, subtracted, multiplied, and divided)
Which is the average: mean, median, mode, range?
Mean
(The mean is the average of a set of two or more numbers and to get it you add all the numbers together and then divide by how many numbers in the set)
Which of these describes a square root function?
a) y = cbrt of x
b) y= sqrt of x
c) x = sqrt 1
d) y = x sqrt 2
b
(Square root functions are sqrt x’s in graphs. They start at 0,0 go to the left, gradually increasing in slope)
Is this a stretch or compression y=⅕(x^2-6) -3?
Compression
(When the coefficient is greater than 1 then it will be a stretch and if it's between 0 and 1 its a compression)
What is end behavior?
End behavior is what x and y is approaching on left and on the right side of the graph
In the radical y sqrt x, which is the radicand
x
(A radicand is a number or variable inside of a radical symbol in this case x which is inside of the sqrt)
What is an inverse variation?
As x increases, y decreases
(Used to find relationships between variables shown by y=k/x)
What would a quadratic equation look like on the graph if it had a reflection?
It would look like an upside down U
(When an equation has a reflection the equation will have a negative at the beginning and flip on the x axis)
What is the parent function for an exponential equation?
y=b^x
(The exponential function is used to find the exponential growth or decay in a set of data)
In which unit did we learn about piecewise functions?
Unit 1
(Piecewise functions are the distance from zero on a number line written algebraically)
What is the imaginary root theorem?
Complex roots always come in pairs
(Imaginary root theorem is used to find all rational roots of a polynomial)
What is the formula for the nth term (Arithmetic)?
an=a1+(n-1)d
(This formula is used to find any number in an arithmetic sequence as long as you have a1(first term in a sequence) and d(common difference between terms)
Which of the following is a quintic polynomial
a)x^2 + x + 5
b)2x^3 + x^2 + 7
c)5x^5+3x^4+8x^3+4x^2-9
d)3x^4 – 2x^3 + x^2 + 8
c
(polynomials are functions that two or more algebraic terms and in this case it's a quintic polynomial which has 5 algebraic terms)
What are the steps in solving a cube root function?
First you isolate the radical. Then you cube both sides to eliminate the radical followed by solving the equation by isolating the variable. Finally you check all solutions in the original equation.
(Cube root functionsx are cbrt x’s in graphs. The make an s shape and pass through 0,0)
What are the steps of completing the square?
1. Set equal to C | 2. Add (b/2)^2 to both sides | 3. Identify the perfect square trinomial | 4. Factor | 5. Find the vertex | 6. Solve
(Completing the square is used to find the vertex of a quadratic equation or just solve a quadratic)
Solve using synthetic division: 3x^3 - 4x^2 + 5x - 7 for x=2
3x^2+2x+7 + 11/x-2
(You use synthetic division when you need to divide a polynomial by a binomial and to solve you taking the coefficients and set them up in rows and start it with the opposite of x= which in this problem is -2)
Are there any holes in this rational equation? (x+5)(x+15)/x+5?
Yes, 1 hole
Solve the equation for absolute value
-3|2a-6|+4=16
(First you -4 on both sides followed by dividing both sides by -3 to isolate the absolute value getting 2a-6=-4. Then you make the same equation but with the = opposite giving us 2a-6=4. Finally you solve for a in both equations by adding 6 then dividing by 2 to get the answers 1 and -5)
Which quadrants are the branches of y=1/x in?
Quadrant 1 and 2
(Reciprocal functions are 1/x’s in graphs. They have two lines which start at x=0 and increase or decrease depending on the line)
What is the standard form of a line? (unit 1)
Ax+By =C
(You use the standard form of a line when a linear equation has two variables. ex: 5x-3y=7)
Solve 3x+4y =12, 2x+y=10 using elimination
y=1.2 x=5.6
(Start by putting both equations in standard form. Then make the coefficients of one variable opposites and add to eliminate the variable. Finally solve for the remaining variable and plug it in to the equations)
Find the 10th term in the arithmetic sentence -3,-5,-7,-9…
-21
(You use the formula an=a1+(n-1)d to get and find a1(first number in sequence), n (number your trying to find), and d (common difference between terms). a10=-3+(10-1)-1=-21)