FUNctions Flashcards
What’s wrong with PEMDAS?
Multiplication doesn’t come before division. Work left to right! And Addition does not come before Subtraction. Work left to right!
What is it called when you add something to both sides of an equation?
Addition Proptery
What property? 3x + 4 - 4 = 12 - 4
Subtraction Property
Solve: -5 < x + 1 < 4
-6 < x < 3
When graphing an inequality, fill in the circle if…
The inequality is greater then or equal to / less then or equal to.
What is absolute value actually asking?
Distance to zero (which is always positive because distance must be positive).
Solve: | 3x + 2 | = -4
No solutions. (Because distance to zero cannot be negative).
What is a function?
A relation in which ever input creates only one output.
Every function can be graphed using what strategy?
A table of values. For every x (left/right) input there is a matching y (up/down) output value.
What is the slope formula?
y - y over x - x (rise/run is a good mnemonic but is not a formula)
How is the slope of a straight line classified?
Positive, Negative, or Zero
A positive slope…
rises as you read the graph from left to right.
A vertical line has what kind of slope?
Undefined.
Slope intercept form is:
y=mx+b
The m in y = mx + b represents:
slope
The b in y = mx + b represents:
y-intercept
The x and y in y = mx + b represent:
Every point on the line.
What is the point slope form for a line?
y - y1 = m(x-x1)
What does the graph of an absolute value function look like?
A V.
What does the 4 and 2 do in the graph: y = |x +4| -2
4 is a left shift. -2 is a down shift.
When do you use a dotted line in a linear inequality graph?
When the inequality is not “or equal to.” 3x-2y > 2
How many solutions can a linear system of equations in 2 variables have?
One (intersecting), zero (parallel), or all solutions (stacked identical lines).
What is the slope of perpendicular lines?
Opposite receptacles. Such as 2/1 and -1/2
What are the two ways to solve linear systems algebraically?
Substitution & Elimination
How do you add or subtract matrices?
Just mash together corresponding values. Easy.
What is the determinate of a matrix?
The difference of the products of the diagonals.
What is end behavior?
What’s happening toward the far left and right of a graph.
What is the quadratic formula?
-b +- sqrt (b^2 - 4 ac) all over 2a
What are the solutions like if the discriminant is negative?
Imaginary roots
What do we use synthetic division for?
Pulling factors (x-k) out of a polynomial with division. (Using rational zeros theorem).
What is rational zeros theorem?
All possible real roots are in the set of factors of the constant term over factors of leading coefficient.
What is a polynomial function.
Function with decreasing exponents.
What is a local maximum and minimum?
The peak and valley in a certain interval.
What are like terms
Terms that have the same variable part.
What are the two strategies for dividing polynomials?
long & synthetic
