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Ch 2-Functions and Graphs
Ch 3-Linear and Quadratic functions
Ch 4-Polynumial and Rational Functions
Ch 5-Exponential and Logarithmic Functions
Ch 6-Trigonometric Functions
100
What is the domain of F(x) = √ (x-3) / (x-2)
D = {x|x ≠ 2, x >= 3}
100
What are the vertical asymptotes, if any, for f(x) = x+2/ (x^2)-4
x=2
100
The points at which a graph changes direction (increasing to decreasing or vise versa) are called _____.
Turning points.
100
Find the inverse of f(x) = 4x + 2
F(x) = x/4 - 1/2
100
Given the polynomial: f(x) = 2x^4 + 4x^3 - 9x^2 +x -2 What is the maximum number of zeros? What are all the possible rational zeros?
Max number of zeros: 4 Possible rational zeros: + or - (1, 1/2, 2)
200
f(x)= 2(x^2) / (x^4) +1 If f(x)=1, what is x? In ordered pair(s).
(-1, 1) (1, 1)
200
Determine whether the function has a maximum or minimum value. What is the value? f(x) = -3(x^2)+12x+1
Maximum value at 13.
200
Find vertical and horizontal or oblique asymptotes of f(x) = (x^3) - 8 / (x^2)-5x+6
VA: x=3 OA: y=x+5
200
Solve Log3 (4x-7) =2
x=4
200
If theta is an angle in standard position, and (x,y) is the point where the terminal side of theta intersects the unit circle and is r units from the origin, how is CSC(theta) defined?
r/y
300
Is this function even, odd, or neither? f(x) = -(x^3) / 3(x^2)-9
Odd
300
What is the name of the vertical line that contains a quadratic function's vertex?
Axis of symmetry.
300
Solve 2x^3 > -8x^2
(-4, 0) U (0, infinity)
300
If m(x)=3ln(x^2 + 4) define functions f and g such that m(x)=f(g(x)).
Answers may vary: f(x) = 3lnx g(x) = x^2 +4
300
Tan(x) = 1/2 and sin(x)<0 Find sin, cos, CSC, sec, and cot.
Sin(x) = -√ 5 / 5 Cos(x) = -2√ 5 / 5 csc(x)= -√ 5 Sec(x)=-√ 5 / 2 Cot(x) = 2
400
State the vertical/horizontal shift, the vertical stretch, and whether the graph opens up or down: f(x) = 2(x^2)-12x+19
f(x)=2(x-3)^2 +1 Vertical stretch: 2 Horizontal shift: 3 Vertical shift: 1 Opens up.
400
Solve (x-2)^2 / (x+2)(x-5) > 0
(-infinity, -2) U (5, infinity)
400
Find the domain, x-intercept, y-intercept, vertical/horizontal/oblique asymptotes, and where the graph is positive and negative. (Hint: make a table) f(x) = (x^2)+x-12 / x+2
D: {x|x ≠ -2} x-int: (-4,0), (3.0) y-int: (0,-6) VA: x = -2 OA: y=x-1 (-infinity, -4) negative (-4, -2) positive (-2, 3) negative (3, infinity) positive
400
An exponential function is in the form f(x)=b^x. What are the restrictions on b? How would y=b^x be written in log form?
b > 0 b ≠ 1 x = logb (y)
400
Find the exact value: Sec(cot-1(-1/2))
-√ 5
500
What is the average rate of change of f(x) = (x^2) -x +4 from x=1 to 3. What is the difference quotient of the function?
Rate of change: 3 Difference quotient: 2x+h-1
500
f(x) = [ -32(x^2) / (50)^2 ] + x + 200 What is the horizontal distance where the height is at maximum?
625/16 Approximately 39.
500
If f is a polynomial such that as x approaches negative infinity, f(x) approaches positive infinity, and as x approaches positive infinity, f(x) approaches negative infinity, what is true about the degree of f? Do you know anything about the function's coefficients?
The degree is odd. The leading coefficient is negative.
500
If [ f(x) / x-c] = q(x) + [r / x-c] (that is, you divide f(x) by x-c and get a quotient q(x) with a remainder of r), what is f(c)? What theorem is this?
r The remainder theorem.
500
What is the range of CSC-1(x) and sec-1(x)?
csc-1(x): [-pi/2, pi/2] not 0 Sec-1(x):[0, pi] not pi/2