Pre-Calc Tests 4, 5, 6, 7
Evaluate (sin(11pi/6) - tan(5pi/6))*(sin(11pi/)+tan(5pi/6))
(a) -1/12
The graphs of f(x) and g(x) are shown below. Find the value of g(f(2))-f(g(2)).
(a) -2
If f(x)=cbrt(9x+1), find f^-1(-1)
(a) -2/9
Solve 5/2x - 5/3(x+5) = 5/x
(a) -3
Eliminate the complex fraction: (x^-1 + y^-1)/x+y
(a) 1/xy
Solve for x: ln(x+6)-ln2=-1
(a) 2/e -6
Which of the following functions are odd? I. f(x)=cos x/x^3+x II. g(x)= x-sin x/e^x - e^-x
(a) I only
Using the figure below, find the equation of the line perpendicular to the given line passing through the given point.
(a) x+3y=3
The graph below left is y=f(x) and the graph below right is a transformation of f(x). What is a possible equation for the graph transformation?
(a)-2f(x-1)
1/x^3+1 + 1/x^2-1
(a)x^2/(x-1)(x+1)(x^2-x+1)
What is the domain of y=sqrt(5x+25)/x^2-25
(b) (-5, 5)u(5, inf)
If y=cbrt(x-1)/sqrt(-2x-4)
(b) (-inf, -2)
Completely factor x^3-xy^2+x^2y-y^3
(b) (x+2)^2(x-y)
Two functions f(x) and g(x) are defined at x = 7 by the table below. f(x) is an even function and g(x) is an odd function. A 3rd function h(x) is defined by h(x)=f(x)-g(x). What is the value of h(-7)? x | f(x) | g(x) y | -5 | 2
(b) -3
{sqrt(x+2)-2 when x>= 2, If f(x)={x^2-1 when 0<=x<2 {-x when x<0 Find sqrt(5-f(-4))
(b) 1
Eliminate the complex fraction (x^-2+x^-1+1)/(x^-2-x)
(b) 1/1-x
Evaluate (cos(2pi/3)-tan(3pi/4))^2
(b) 1/4
Find e^ln(12)
(b) 12
Find log3(sqrt(3))5
(b) 5/2
Consider the set of all roots of the equation 2sinx*cosx-cosx+2sinx=1 on [0, 2pi). What is the difference between the largest and the smallest root?
(b) 5pi/6
If AB _|_ CD what is the perimeter of the triangle ABC?
(b) 6+2sqrt 3
Which is true about the following equations? I. |1-3x|=1 II. |2x+5|+3x=0 III. |x^2-x-1|=5
(b) I&III have 2 solutions, II has 1 solution
Which of the functions below is an even function? I. f(x) = x^3-x+1 II. f(x) = |x^3| III. f(x) = 2^x
(b) II only
Place these three values in order from largest to smallest. I. log25(1) II. log25(1/5) III. log125(25)
(b) II, I, III
Simplify 1/4(16x^2)^-3/4 (32x)
(b) sqrt(x)/x
The inverse of the function to the right is
(b) y=-3+-sqrt(x)
-2x^-3 - x^-2 / x^-2 + x^-1
(b)-x-2/x(x+1)
Simplify (-27x^-3*sqrt(z)/8y^6)^-2/3
(b)4x^2y^4/9cbrt(z)
Solve for x: f(x) = 2cosx+1/2sinx-sqrt(3)>0
(c) (pi/3, 2pi/3)u(2pi/3, 4pi/3)
If csc theta = 6/5 in quadrant II, find cos theta.
(c) -sqrt(11)/6
Simplify x^-2-y^-2/x-y
(c) -x-y/x^2*y^2
Below are 6 functions. If E is the number of even functions and O is the number of odd functions, what is the value of E^-0 (E raised to the negative O power)? I. f(x)=x^2 II. f(x)=x^3 III. f(x)=1/x IV. f(x) = e^x V. f(x) = sin x VI. f(x) = cos x
(c) 1/8
If the equation 4^3x-1=(1/2)^1-2x is solved for x, which of the following is the largest?
(c) 1/x
Let the point (15, 8) be on the terminal side of theta. Find csc (theta).
(c) 17/8
If a is the number of solutions to the equation |4x|=12 and b is the number of solutions to the equation |6-3x|+x=0, what is the sum a+b?
(c) 2
If f(x) = 2pi(x+1)^2, what is f(2a)-f(a)
(c) 2pi(3a^2+2a)
The equation of the line passing through (-3,2) perpendicular to the line 3x-4y=1 is
(c) 4x+3y=-6
1/(x-3)+1/(x+3)=10/(x^2-9)
(c) 5
Find the largest value.
(c) 5sec(5pi/3)
Which of the following expressions are greater than 1? I.(3/2)^-3/2^-2 II.(4/9)^-1/2/(8/27)^-2/3
(c) I & II
Given tan(theta) = 3/4, theta in quadrant III, arrange each of the following in order from largest to smallest. I. sin(theta) + cos(theta)/sin(theta)+2 II. (sin(theta)+cos(theta))^-1 III. (cot(theta)-tan(theta))^1/2
(c) III, II, I
Determine the quadrant where csc theta < 0 and cot theta > 0 is true.
(c) Quadrant III
State the vertical asymptotes (VA), horizontal asymptotes (HA) and holes, if any, of y=(4+3x-x^2)/3x^2
(c) VA at x=0 and HA at y=-1/3
Find an equation of the line containing (4, -2) and parallel to the line containing (-1, 4) and (2, 3). Put your answer in general form.
(c) x + 3y + 2 = 0
Simplify x^-2-x^-4/x^-2-x^-1
(c)-x-1/x^2
4/a-b - 5/a+b
(c)9b-a/a^2-b^2
Factor x^4-x^3-x+1
(d) (x-1)^2(x^2+x+1)
If f(x) = x^2-8x+3, find the slope of the line between (x-h, f(x-h)) and (x+h, f(x+h))
(d) 2x-8
If f(x)=x^3, find f(x+h)-f(x-h)/2h
(d) 3x^2+h^2
Evaluate cot^2 135 - sin 210 + 5cos^2 225
(d) 4
If V(r) = 4/3*pi*r^3, find V(2r)/V(r)
(d) 8
Which of the following equations are identities? I. sin x (csc x - sin x)=cos^2 x II. tan x + cot x = sec x * csc x III. 1 - sec x / 1 - cos x = sec x
(d) I&II only
If x=-5, arrange the following from highest to lowest. I. (-1/2x)^-1 II. (4/x^2)^-3/2 III. (-8/x^3)^-2/3
(d) II, I, III
State the vertical asymptotes (VA) and horizontal asymptotes (HA) of y=1/x - x/x+2
(d) VA at x= -2, 0
Solve for x: 2x+6/x+1<=x
(d) [-2, -1)u[3, inf)
The graph of sin x is odd and the graph of cos x is even. If f(x) = sin x + cos x and g(x) = sin x*cos x, which of the following is true?
(d) f(x) is neither even nor odd, g(x) is an odd function
Find k if the lines 3x - 5y = 9 and 2x + ky = 11 are perpendicular
(d) k = 6/5
Solve for X: x^2+10x=7
(d) x = -5 +- 4*sqrt(2)
Simplify (4x^-1)^-1
(d) x/4
Solve for x: x^3-5x^2+5x-25=0
(d) x=5
Which of the following cannot be factored?
(d) x^2-8x-16
Which of the following has a positive root?
(d) y=-ln x Root: x=1
Which of these is not equal to [0,inf)?
(d) y=e^x, R: (0, inf)
Which of the following functions does not include x=4 in its domain?
(d) y=x+4/x^2-16
If y=2x^2-kx+3, for what value(s) of k will the quadratic have 2 real solutions?
(e) (-inf, -2sqrt6)u(2sqrt6, inf)
Find the difference between the greatest and smallest root of 1/x-3 - 2x+3/(x-3)^2 = -10/(x-3)^3
(e) 11
Let P(-4,3) be a point on the terminal side of theta. Arrange these expressions from highest to lowest value.
(e) III, II, I
Which of the following is true about these three values? I. log7(3)+log7(48) II. 2log7(12) III. log7(12)-log7(1/12)
(e) They're all the same value
Fin all asymptotes for f(x)=1-x/x^2-1
(e) VA at x=-1, HA at y=0
If f(x)=x^2-5x-4 and g(x)=|1-x|, which has a value different from all the others?
(e) f(g(0))
The equation 2log2(x+1)-log2(x)=2 has a solution of x=1. What can be said about other solutions to the equation.
(e) no other solutions
Completely factor 3x^8-3
(x) 3(x^4+1)(x^2+1)(x+1)(x-1)
Simplify (-32x^-5)^-3/5
-x^3/8
