Review Sheet Advanced Function Midterm Ms. Boyle 1. Simplify: !!!
d. 3 − 2𝑖 −6 + 5𝑖 a. !!!! !!
e. !! b. 3𝑖 + 6𝑖 c.
−9— 81 2. Find the equation of a line passing through (3, 7) and (-­‐2, 5). !
3. Given the equation 𝑦 = − ! 𝑥 + 4 a. Find the slope of a parallel line b. Write the equation of a parallel line that passes through (9, 13) c. Find the slope of the perpendicular line d. Write the equation of a perpendicular line that passes through (-­‐2,5) 4. Factoring fun! a. x 3 = x d. x 2 = 21x + 100 2
b. x 2 − 3x + 1 = 0 4 ( x − 5) = 24
e.
c. x 2 = −81 5. Determine the maximum and minimum of the functions given. Determine the x and y intercepts. Determine when the function is increasing and decreasing. Determine the end behavior of each function. 1
a. y = − ( x − 4)( x + 8) 4
2
b. y = x + 5x −14 c. 𝑦 = 𝑥 ! − 4𝑥 6. Determine the domain and range of each of the following. Determine the end behavior of each function. !!!
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a. 𝑦 = 3! c. 𝑦 = ! b. 𝑦 = log𝑥 d. 𝑦 = 2 − 𝑥 7. Draw a sketch (if possible) of a parabola that satisfies the characteristics below. a < 0 c > 0 b
− < 0 b2 − 4ac > 0 2a
8. Find the equation of a polynomial described: a. With root −2i
b. With a triple root at -­‐2 and a double root at 5 that passes through (3,50) c. parabola has a minimum at (-­‐2,7) and passes through the point (2, -­‐4) 9. Simplify: a. 𝑥 !! ! # 15c 7 d −14 & 3
! !
d. %
( !
b. ! 45c −7 d −12 '
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!
c. 64 x−1 = 16 x +2 €
e.
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2
7 5 = 49 4 x−3 f.
8 x = 2 6 i.
1
3
g. x = 2 h. x14 2 ⋅ x 7 2 ⋅ x −3 2 10. Solve: a. log 3 5 9 €
1
b. log x 3 = 4
c. log x (3 − 4 x) = 2 €
3
d. log x 27 = 2
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j.
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100 x = 10 x + 6 " 1 %−3
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1
1
log 81− log 27 2
3
log 7 x + log 7 ( x − 6 ) = 1 e. log x =
f.
g. log 7 x = 4 log 7 2 + ( log 7 3 − log 7 6 )
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!
11. Given 𝑓 𝑥 = !!!, 𝑔 𝑥 = 𝑥, and ℎ 𝑥 = 𝑥 ! a. find the domain of f(x), d. find h(g x ) g(x), and h(x) e. find the domain of each b. find f(g x ) of the composite you c. find f(h x ) found 12. Given 𝑔 𝑥 = 𝑥. a. find the domain and c. find the domain and range of g(x). range of 𝑔!! (𝑥) b. find 𝑔!! (𝑥) 13. Sketch the piecewise functions 𝑥 + 2, 𝑥 < 3
𝑥 ! + 1, 𝑥 > 0
a. 𝑓 𝑥 =
b. 𝑔 𝑥 =
! 7 − 𝑥 , 𝑥 ≥ 3
1 − 4𝑥, 𝑥 < 0
14. Sketch the transformations of the original function. Note these building on each other. a. 𝑓 𝑥 − 1 b. – 𝑓 𝑥 − 1
!
c. − ! 𝑓 𝑥 − 1
Be prepared to classify a function, find the x and y intercepts, local maximums and minimums, and determine when the function is increasing and decreasing. Be prepared to know the relationship between degree of a function and the number of zeros or maximums and minimums a function has.