ALGEBRA FINAL REVIEW
GRAPH the RATIONAL FUNCTION showing all of the steps discussed in class
1. DOMAIN-set BOTTOM to 0 DO QUAD 2. X-int-set TOP to 0 DO QUAD 3. Y-int C/C DIVIDE CONSTANTS 4. VA SEE WHATS LEFT FROM DOMAIN- was it used already if so there is a HOLE 🕳 5. HA LOOK AT LEADING TERM(EXPONENTS) If same divide If top big NO HA if bottom big Y=0
find vertical asymptote (VA) if any of the graph of the ration function
1. Domain 2. X-int: top=0 X^2-36=0 +36. +36 —————— sq rt/x^2 = sq rt/36 X= plus or mine 6 VA IS X=6 VA IS X=-6
Find the domain of the function g(x)=x^2-2 ———————— 4-x^2
4-x^2=0 +x^2 +x^2 ————————— Square of 4 = sq rt of x^2 ANSWER: x=plus or minus 2
GRAPH to determine the functions domain and range GRAPH IS A PARABOLA with (-3,-3) endpoint
DOMAIN: (-♾, ♾) RANGE: [-3,♾) REMEMBER BRACKET THATS THE ENDPOINT
Does the graph represent a function that has an inverse function?
HLT-HORIZONTAL LINE TEST graph show backward s Parent function 3/sq rt of x YES IT PASSES THE TEST (it does hit more than once)
Find the HORIZONTAL ASYMPTOTE if any of the graph of the rational function
LOOK AT EXPONENTS if same divide If top big NO HA If bottom big Y=0
find Horizontal Asymptote (HA) if any of the graph of the ration function
LOOK AT EXPONENTS! SAME-DIVIDE TOP BIG-NO HA BOTTOM BIG- Y=0
Use the RATIONAL ZERO THEOREM to list all possible rational zeros for the given function
P/Q C/LC FACTOR ONLY
Find a rational zero of the polynomial function and use it to find all the ZEROS OF THE FUNCTION-(aka find x-intercepts)
P/Q aka C/LC FIND FACTORS PLUS OR MINUS THE FACTORS SYNTHETIC DIVISION once you get to x^2+x+1 DO QUAD. FORMULA
EVALUATE the function at the given value and simplify f(x)=4x^2-5; f(x+2)
PLUG IN (x+2) into X THEN FOIL (x+2) Should get 4(x^2+2x+2x+4)-5 4x^2+8x+8x+16-5 ANSWER: 4x^2+16x+11
GRAPH the POLYnomial function showing all of the steps discussed in class
POLY-is 3 1. END BEHAVIOR: Right Left 2. X-int P/Q-FACTOR-plus or mine FACTOR QUADRATIC FORMULA 3. Y-int IS THE CONSTANT
Find and simplify the DIFFERENCE QUOTIENT f(x+h)-f(x)/h, h≠0 for the given function f(x)=3x^2-4
PUT IN (x+h) for x^2 FOIL (x+h)^2 should get 3(x^2+xh+xh+h^2)-4 COMBINE XH 3(x^2+2xh+h^2)-4 PUT IN TO FORMULA 3x^2+6xh+3h^2-4/h-3x^2+4 REMEMBER TO DISTRIBUTE THE NEGATIVE CANCEL THE H should be left w/h ANSWER: 6x+3h
Find the INVERSE of the one-to-one function f(x)= 3 —————- 8x-5
REMEMBER ——> 1 to 4 1. Change f(x) to y 2. Swap y's and x's 3. SOLVE FOR Y 4. Change y to f-1(x)
Use the LEADING TERM TEST to determine the END BEHAVIOR of the polynomial function
RIGHT - LEADING TERM LEFT - EXPONENT
f and g, find (fog)(x)
f(x)=3/x-5, g(x)=1/7x f(x)=3 ————— (1/7x)-5 Multiply denominator f(x)=3(7x) —————— (7x) (1/7x)-5 (7x) ANSWER: 21x ——— 1-35x. <——-remember the 1
Find gof and the state the domain of the composite function gof
f(x)=x+3, g(x)= 1/x+7 PLUG f(x) into g(x) 1 1 1 ——- ——— = ———- (x+3)+7 = x+3+7 x+10 SET answer to 0 (x+10) X+10>_0 -10. -10 ——————- X>_ -10 D: (-♾,-10) U (-10,♾)
GRAPH the cubic standard form f(x)=x^3 And Use transformations
g(x)=-(x-2)^3 +3 1. Parent function X^3 (twisted parabola) ⬇️⤴️ 2. FLIP OVER X -(x-2)^3 3. MOVE OVER 2 (remember it's opposite) so it will would be positive 2 4. MOVE UP 3
VLT
⬅️↩️↪️ graph look like a backward s hits💥 3 times on the y axis NOT A FUNCTION
