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Description
Flashcards by Lance Erickson, updated more than 1 year ago
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Created by Lance Erickson
about 7 years ago
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| Question | Answer |
| A 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 |
| A 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 |
| Use 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 |
| What 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} |
| DON'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. |
| What 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 |
| What are the steps to solve the equation: | clean up ( +5 ), power 4/3 each side check answer with graphical method |
| What 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 |
| What are the steps to solve the equation: | “= 0”, factor: find a zero then synthetic division continue until you have quadratic and use formula |
| steps to solve? | clean up ( - x ) square both sides (FOIL left) formula or factor (since x^2) |
| DON'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 |
| clean up ( -2) , power 4, then use formula since it is now a quadratic check answer with graphical method | |
| clean up (-4), power both sides by -5 to get x alone check answer with graphical method | |
| 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 | |
| a) 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) |
| DON'T DO: | Switch x and y and solve for y! Subtract 4, power both sides by -5. inverse is = ( x - 4)^ -5 |
| Switch x and y and solve for y! Cube both sides, add 4, divide by 2 inverse is = (x^3 + 4)/2 | |
| the 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 |
| Sketch the function if a < 0, b = 2, and d = 1 | There 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! |
| Sketch the function if a > 0, b = 1, and d = 2 | There 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! |
| 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 | |
| How would you solve both graphically and algebraically | Algebraically: 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 |
| The digdogit is inversely proportional to the square of slippitdoodah. If 5 slippitdoodahs produce 17 digdogits, then how many digdogits come from 12 slippitdoodah | Kyx, 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 |
| The digdogit is proportional to the square root of slippitdoodah. If 5 slippitdoodahs produce 17 digdogits, then how many digdogits come from 12 slippitdoodah | Kyx, 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 |
| The digdogit is inversely proportional to the cube root of slippitdoodah. If 5 slippitdoodahs produce 17 digdogits, then how many digdogits come from 12 slippitdoodah | Kyx, 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 |
| This is asking about end behavoir: Degrees: 3/1 so end behavior y goes to negative infinity . | |
| This is asking about end behavoir: that is, the HA = -2 | |
| This is asking about end behavoir: that is HA = 0 (the x axes) | |
| Write down a function that has an x intercept x = 1 and x = 0, a vertical asymptote x =2 and horizontal asymptote y = 10. | |
| Write 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! |
| DON'T DO:Describe how you can find the equation of an exponential function from it’s graph | |
| DON'T DO:Describe how you can find the equation of an exponential function from a table. | |
| DON'T DO:Describe how you find the inverse of a function from a) a table b) a graph c) an equation | a) 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! |
| DON'T DO:how can you determine if a function has an inverse from: a) it’s graph b) the table c) a function | a) it passes the horizontal line test b) no y’s are repeated. c) if degree is even then not. Otherwise, graph and see |
| how to solve an equation graphically? | Graph "both sides" of the equation. find the x coordinate of point of intersection |
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