Complex Numbers
Evaluate i^862 without a calculator.
-1
Determine the vertex and end behavior of the following quadratic function.
f(x) = -2x^2 + 4x - 1
Vertex: (1, 1)
End Behavior: Fall to the left, Fall to the right
Find the domain of the following function
f(x) = (4 - 2x)/(5x - 1)
(- infinity, 1/5) U (1/5, infinity)
DOUBLE JEOPARDY!!
Find f(-2) given the following exponential function.
f(x) = -4^(2x + 3)
-1/4
Convert 13pi/9 radians to degrees.
260 degrees
Perform the indicated operation for complex numbers and express your answer in a + bi form.
(2 - 3i)(3 + 6i)
24 + 3i
Determine the possible number of positive and negative real zeros.
f(x) = π₯^4β3π₯^3+6π₯^2β4π₯β12
3 or 1 Positive Real Zeros
1 Negative Real Zero
Find the x and y intercepts
f(x) = (x - 6)/(x^2 + 4)
x- intercept: (6, 0)
y- intercept: (0, -3/2)
Solve for x by converting the logarithmic equation to exponential form.
log_2 (x) = -3
x = 1/8
Convert 160 degrees to radians.
8pi/9 radians
DOUBLE JEOPARDY!!
If f(x) = 2x^2 + x - 3, find f(i)
-5 + i
Find all zeros and their multiplicity
f(x) = (x^2 + 2x + 1)(2x - 7)^3
x = 7/2, multiplicity 3
x = -1 multiplicity 2
Find the horizontal and vertical asymptotes
f(x) = (-2x + 4) / (3x - 1)
Horizontal Asymptote: y = -2/3
Vertical Asymptote: x = 1/3
Solve the equation
5log_7 (x) = 10
x = 49
State the coterminal angle for 13pi/4 radians
5pi/4 radians
Perform the indicated operation for complex numbers and express your answer in a + bi form.
(3 + 4i) / (2 - i)
2/5 + 11i/5
Divide the following polynomials using synthetic or long division.
(π₯^4 β 8π₯^3 + 24π₯^2 β 32π₯ + 16) Γ· (π₯ β 2)
π₯^3 β 6π₯^2 + 12π₯ β 8
Find the x and y intercepts, and vertical/horizontal asymptotes.
f(x) = (x^2 - 4x + 3) / (x^2 - 4x - 5)
x-intercept: (1, 0), (3, 0)
y-intercept: (0, -3/5)
Horizontal Asymptote: y = 1
Vertical Asymptote: x = 5, x = -1
State the domain, range, horizontal asymptote. and y-intercept for the given exponential function.
f(x) = 2^x + 3
Domain: (-infinity, infinity)
Range: (3, infinity)
Horizontal Asymptote: y = 3
y-intercept: (0, 4)
Find the length of the arc of a circle of radius 12 miles subtended by the central angle of 140 degrees.
(Exact Answers)
28pi/3 miles
If f(x) = (x + 1) / (2 - x), evaluate f(5i). Write your answer in a + bi form.
-23/29 +15i/29
Find all zeros of the following polynomial.
f(x) = π₯^3 β 8π₯^2 + 25π₯ β 26
x = 4, 3 + 2i, 3 - 2i
Find the slant asymptote.
f(x) = (4x^2 - 10) / (2x - 4)
y = 2x + 4
State the domain, range, vertical asymptote and x- intercept of the given logarithmic function
f(x) = log_4 (x - 1) + 1
Domain: (1, infinity)
Range: (-infinity, infinity)
Vertical Asymptote: x = 1
x-intercept: (5/4, 0)
Find the area of a sector of a circle that has a central angle of 30Β° and a diameter of 40 cm.
(Round to two decimal places)
104.72 cm^2