Karteikarten
polynomials review
Karten in diesem Stapel (35)
- 1A polynomial of degree 4 has zeros of x = 2, x = 4i and and f(-5) < 0 Write a function in factored form.Answer
f(x)= - (x-2)^2 (x-4i) (x+4i)
notice the square. Since the degree is 4 and imagainary's only come in pairs…..
also notice the leading coefficient is negative to ensure that f(-5) < 0.
Try a quick sketch to see - 2A polynomial of degree 3 has zeros of x = 2, x = -6i and f(0) < 0 Write the function in standard form.f(x) = (x-2) (x-6i) (x+6i)
Then FOIL. Start with the imaginary factors when foiling.
x^3 - 2x^2 + 36x -72
note it is "+" to make sure f(0) < 0 - 3Use the numerical representation of the function f(x) to answer the questions: a) Use the table to find f (f(2). b) DON'T DO:find the equation and use that to find f (f(2).put in "2" then answer back in.
f(2) = 6 and f(6) = 162
equation: y = (2/3) 3^ x - 4What is the range of f(x) ? What is the domain of f(x) ?Range of inverse is domain of function: {-1,0, ……6}
Domain of inverse is range of function {2/9……162}
- 5DON'T DO:Does this function have an inverse? Explain why. How can you tell if it were a graph?Yes as y values do not repeat. i.e. it is one to one
For a graph it has to pass the horizontal line test.
- 6What are the steps to solve the equation:clean up ( +6 ), square both sides (FOIL right side)
solve with formula since it will be x^2
- 7What are the steps to solve the equation:clean up ( +5 ), power 4/3 each side
check answer with graphical method
- 8What are the steps to solve the equation:“= 0”, factor out x (which tells you 0 is an x intercept) then use formula or:
find a zero then synthetic division
continue until you have quadratic and use formula
- 9What are the steps to solve the equation:“= 0”, factor: find a zero then synthetic division
continue until you have quadratic and use formula
- 10steps to solve?clean up ( - x )
square both sides (FOIL left)
formula or factor (since x^2)
- 11DON'T DO: what are the steps to solve this equation?clean up ( + x ), square both sides (FOIL)
clean up again then square again (FOIL)
solve (probably use the formula)
check answer with graphical method
- 12—clean up ( -2) , power 4, then use formula since it is now a quadratic
check answer with graphical method
- 13—clean up (-4), power both sides by -5 to get x alone
check answer with graphical method
- 14—factor denominator
multiply by x(x-9) to remove fractions
solve maybe need formula. Also, watch for “minus“ in middle
check answer with graphical method
- 15a) what is the zeros and their multiplicities b) What is the degree? c) Fill in the blank with <, > , = : “a” ____ 0 d) Find f(f(3)) e) Solve for x given f(x) =5 f) Solve for x given f(x) > 5 g) write down a possible equation for the polynomial.a) x = -2 (multiplicity of 3), x = 1 (multiplicity of 2), x = 3 (multiplicity of 1)
b) degree 6
c) a < 0 right side “down”
d) f(3) = 0 and f(0) = 2.5
e) x =1.9
f) (1.8, 2.8)
- 16DON'T DO:Switch x and y and solve for y!
Subtract 4, power both sides by -5.
inverse is = ( x - 4)^ -5
- 17—Switch x and y and solve for y!
Cube both sides, add 4, divide by 2
inverse is = (x^3 + 4)/2
- 18the function f(x) is shown. Sketch g(x) = 3f(x) -1 g(x) = 0.5f(x-1) g(x) = 0.5 + f(3x) g(x) = 7f(0.5x)take points from the graph and then:
1) 3 times y then – 1
2) 1 + x then .5 times y
3) 1/3 times x then 0.5 plus y
4) 2 times x and 7 times y
- 19Sketch the function if a < 0, b = 2, and d = 1There are x intercepts at 0 (bounces here!) and 2. right side is negative ( since a < 0).
VA (wall) at x = 4. Sketch and make points when needed.
use calculator or desmos to check!
- 20Sketch the function if a > 0, b = 1, and d = 2There are x intercepts at 0 and 2 (bounces here!). right side is positive.
VA (wall) at x = - 4. Sketch and make points when needed.
use calculator or desmos to check!
- 21—Algebraically: solve: x = 0, 2 and x = -4. Use these on number line and check.
Graphically: graph y = 0 and and see where is the function higher than y = 0
- 22How would you solve both graphically and algebraicallyAlgebraically: solve: x = 0, 2 and VA at x = 4. Use these on number line and check.
Graphically: graph y = 0 and and see where is the function higher than y = 0
- 23The digdogit is inversely proportional to the square of slippitdoodah. If 5 slippitdoodahs produce 17 digdogits, then how many digdogits come from 12 slippitdoodahKyx, pt, sub su:
d = k / s^2
then put in point (17 into d and 5 into s)
solve for k and sub back in
sub in to finish - 24The digdogit is proportional to the square root of slippitdoodah. If 5 slippitdoodahs produce 17 digdogits, then how many digdogits come from 12 slippitdoodahKyx, pt, sub su:
d = k sqrt( s )
then put in point (17 into d and 5 into s)
solve for k and sub back in
sub in to finish - 25The digdogit is inversely proportional to the cube root of slippitdoodah. If 5 slippitdoodahs produce 17 digdogits, then how many digdogits come from 12 slippitdoodahKyx, pt, sub su:
d = k / s^1/3
then put in point (17 into d and 5 into s)
solve for k and sub back in
sub in to finish - 26—This is asking about end behavoir:
Degrees: 3/1 so end behavior y goes to negative infinity .
- 27—This is asking about end behavoir: that is,
the HA = -2
- 28—This is asking about end behavoir:
that is HA = 0 (the x axes)
- 29Write down a function that has an x intercept x = 1 and x = 0, a vertical asymptote x =2 and horizontal asymptote y = 10.
- 30Write down a function that has an x intercept x = 1, x = - 4 , a vertical asymptote x = - 2 and horizontal asymptote y = 0.Note, the cube (or more) in the denominator!
- 31DON'T DO:Describe how you can find the equation of an exponential function from it’s graph
- 32DON'T DO:Describe how you can find the equation of an exponential function from a table.
- 33DON'T DO:Describe how you find the inverse of a function from a) a table b) a graph c) an equationa) switch x and ys
b) reflect over the line y = x (NOT the axes!)
c) switch x and y and solve for y. You should change f(x) to y! - 34DON'T DO:how can you determine if a function has an inverse from: a) it’s graph b) the table c) a functiona) it passes the horizontal line test
b) no y’s are repeated.
c) if degree is even then not. Otherwise, graph and see - 35how to solve an equation graphically?Graph "both sides" of the equation. find the x coordinate of point of intersection
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- 12th grade Math Karteikarten am polynomials review, erstellt von Lance Erickson am 22/03/2017.
- Erstellt von
- Lance Erickson
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