ALEKS MATH PLACEMENT WITH COMPLETE SOLUTIONS 100% 2023/2024

ALEKS MATH PLACEMENT WITH COMPLETE SOLUTIONS 100% 2023/2024 graph ≥, ≤ solid line graph , DOTTED line every, each, per (writing equations) rate/ set y value equal to (multiply this value by the x variable) When writing an equation or working ANY inequality problem what does it help to do first? write out what's happening What should you double check for EVERY time writing problem down wrong (NEGATIVE SIGNS), uncarried negative signs, unflipped inequality signs, undotted lines, incorrect multiplication, fully simplified distance = rate x time When solving a system of equations can you add the equations together if one of the variables will cancel out? YES What should you always write out when doing your work? Fraction conversions, simplification steps, line graphs (interval notation) What standard does an equation/ graph have to meet to be considered a function? Each input can only have one output How do you translate a graph up or down? The value outside of the parentheses (DONT change sign) How do you translate a graph side to side? The value inside the parentheses (CHANGE SIGN) Translate -(x + 3)^3 - 2 from -x^3 left 3, down 2 When translating do you need to solve the equation? No, just look at the numbers inside (side to side change sign) and outside (up and down DONT change sign) the parentheses What is the domain? The x limits What is the range? The y limits U represents Numbers in EITHER set (Union) ⋂ represents Numbers in BOTH sets (Intersection) What is the quadratic formula? -b±√b^2-4ac/2a When asked for the rate, should you give the rate or the rate times the time? THE RATE (x-6)(x+4) 0 Where is the product of (x-6) and (x+4) less than 0? Should you graph two separate equations on the same number line when doing your work? No When you take the square root of a variable, how many answers are there? 2 answers (negative and positive) x^a/x^b x^a-b x^a times x^b = x^a+b (x^a)^b x^ab What should you always physically mark on inequality graphs that are getting compared before attempting to solve the problem? Where the graphs intersect BETC divide the top leading coefficient by the bottom leading coefficient (Bottom Equals Top Coefficient HORIZONTAL ASYMPTOTE) BOB0 the horizontal asymptote = 0 (Bigger On Bottom 0) BOTU there is no horizontal asymptote, find slant asymptote (Bigger On Top Undefined) How do you find the slant asymptote? Divide the ENTIRE numerator by the ENTIRE denominator, the slant asymptote is the quotient, ignore the remainder (might include division with variables raised to exponents) How do you find the vertical asymptote? Set the denominator equal to 0 sin csc cos sec tan cot Can a graph have more than one local maximum or minimum? yes volume cubed area squared perimeter/ length no power How do you find the vertex of a parabola? take the derivative (slope) and set it equal to 0 d/dx (x^a) ax^a-1 antiderivative (x^a) (x^a+1)/a+1