Unit 5
Find the zeros of this equation
y = x(x - 4)(x + 2)
x=0,4,-2
*Zeros are where the graphs hits the x-axis
Find all the real square roots of 0.0081
Answer:
0.09 and -0.09
Write as a single logarithm:
4 log x − 6 log(x + 2)
Answer:
log[x⁴/(x + 2)⁶]
Find the horizontal asymptote of:
y = (4x⁶ − 4x + 12)/(−5x⁶ + 2x + 12)
Answer:
y = −4/5
Which trig graph starts at the center/midline: sine or cosine?
Answer: Sine
Using Synthetic Division to solve
(2x³ + 5x² − 7x − 4) ÷ (x + 2)
Quotient:
2x² + x − 9
Remainder:
14
Simplify this expression:
√(36g⁶)
Answer:
6g³
Solve:
log x − log 6 = 0
Answer:
x = 6
Solve:
1/p + 6/(5p) = 5
Answer:
p = 11/25
What does the period of a trig function tell you?
The period tells how long it takes the graph to complete one full cycle before repeating.
Using FTOA, find the roots of the polynomial equation:
x³ − 4x² − 7x + 10 = 0
Answer:
x=1,5,-2
Bonus: Since our equation is cubic, does the FTOA say there should be three roots of this function?
Find the real-number root of √−3.24.
Answer:
No real root!
Does y = 10(0.58)ˣ represent exponential growth or decay?
Decay, because 0.58 is between 0 and 1.
Write an equation for the translation of y = 4/x that has asymptotes x = −6 and y = 8.
Answer:
y = 4/(x + 6) + 8
Find the period of
y = sin(3x).
Answer:
Use 2π/b.
Here, b = 3.
Period = 2π/3
Find a quadratic equation with roots 2 + 5i and 2 − 5i.
Answer:
f(x) = x² − 4x + 29
Simplify
8²ᐟ³
Answer:
4
A population of 900 quail increases by 34% each year. Write an exponential model.
Answer:
y = 900(1.34)ˣ
Describe the hole and asymptotes of:
y = [(x + 4)(x + 4)] / [(x + 4)(x + 5)]
Answer:
Hole: (−4, 0)
Vertical asymptote: x = −5
Horizontal asymptote: y = 1
What is the amplitude of y = 1/2sin(9x)
Answer: 3
The amplitude tells how tall the wave is from the center line.
Find the number of complex roots and the possible number of real roots for this equation
3x⁵ − 2x³ + 7x − 1 = 0
Answer:
Complex Roots: 5
Possible Number of Real Roots: 5,3,1
*The degree tells you the total number of roots, and imaginary roots come in pairs.
Solve
√(x − 5) + 6 = 10
Answer
x = 21
Suppose you invest $9000 at an annual interest rate of 4.8% compounded continuously. Write the model for the amount after 8 years.
Answer:
A = 1700e^(0.032)(10)
or
A = 1700e^0.32
Solve:
6/(x² − 9) − 1/(x − 3) = 1
Answer:
x = −4
In y = 2cos(x) + 4, what does the + 4 do to the graph?
Answer:
It shifts the graph up 4 units.