Test 2
What is the domain of f(x)=−5x+2−−−−−√−1f(x)=−5x+2−1?
[−25,∞)
What happens to the graph of y=−x6−6x5+50x3+45x2−108x−108y=−x6−6x5+50x3+45x2−108x−108 as xx heads toward ∞∞ and −∞−∞?
as x→∞x→∞, y→−∞y→−∞ as x→−∞x→−∞, y→−∞
How can you find the coefficients of any row of Pascal's triangle?
combinations
Which of the following functions has a vertical asymptote at x=2x=2, a horizontal asymptote at f(x)=1f(x)=1, and a root at x=−1x=−1?
f(x)=3x−2+1
Which of the following functions has a vertical asymptote at x=−2x=−2, a horizontal asymptote at f(x)=−1f(x)=−1, and a root at x=2x=2?
f(x)=4x+2−1
When simplified, the expression (m4−−−√3)m−12(m43)m−12 is equivalent to:
m5−−−√6
If x is a positive integer, the expression (1n)−23(1n)−23 is equivalent to:
n2−−√3
What will be the effect on the graph of y = |x| if x is replaced with -x?
no change
Find the holes of the function (2x−1)(x+4)2(x−1)(3x+2)3x(x−4)(2x−1)3(2x−1)(x+4)2(x−1)(3x+2)3x(x−4)(2x−1)3.
none
Find the horizontal asymptote of the function (x−1)(x−3)2(x+1)2(x−2)(x+2)(x−1)(x+3)(x−1)(x−3)2(x+1)2(x−2)(x+2)(x−1)(x+3).
none
Find the vertical asymptotes of the function −2x(x+3)2(x+2)3x(x+2)(x+3)2−2x(x+3)2(x+2)3x(x+2)(x+3)2.
none
What are the roots of f(x)=2−x−−−√+2f(x)=2−x+2?
none
What are the roots of f(x)=−5x+2−−−−−√−1f(x)=−5x+2−1?
none
What is the behavior of the graph y=−x3−5x2−3x+9y=−x3−5x2−3x+9 at each of its zeros?
one resembles a linear function and one resembles a quadratic function
What effect will replacing xx with (x−4)(x−4)have on the graph of the equation y=(x−3)2y=(x−3)2?
slides the graph 4 units right
Simplify (2x+10)(x2+x−6)4x2+12x−40(2x+10)(x2+x−6)4x2+12x−40.
x+32
What is the equivalent expression of (x3)4(x3)4?
x12
Simplify x2−44x2−12x⋅2x+4−x2+5x−6x2−44x2−12x⋅2x+4−x2+5x−6.
x2+4x+4−2x3+12x2−18x
What is the equivalent expression of (2x3)12+x43−x−1(2x3)12+x43−x−1?
x2x−−√+xx−−√3−1x
What is the lowest common denominator of x−5x2−1−1=−2xx−1x−5x2−1−1=−2xx−1?
x2−1
Simplify x2−44x2−12x÷2x+4−x2+5x−6x2−44x2−12x÷2x+4−x2+5x−6.
x2−4x+4−8x
Simplify 3xy24y⋅2x23y3xy24y⋅2x23y.
x32
What is the equivalent expression of (xy)4(xy)4?
x4y4
What is the equivalent expression of x13x14x13x14?
x7−−√12
The function f(x)=5xf(x)=5x has a vertical asymptote at
x=0
Find the root of the function f(x)=−2x−2−2f(x)=−2x−2−2.
x=1
Solve 12=1x−12x212=1x−12x2.
x=1
Solve 16x2−12x=112x216x2−12x=112x2.
x=1/6
Find the root of the function f(x)=−2x−2−2f(x)=−2x−2−2.
x=1x=1
Solve 3+x5=x+133+x5=x+13.
x=20
Solve 5x2−x−1x=1x2−x5x2−x−1x=1x2−x.
x=5
Find the holes of the function 4(x+2)(x+1)(3x+4)(2x−3)3(x−2)(x2−1)(2x−3)(x+2)44(x+2)(x+1)(3x+4)(2x−3)3(x−2)(x2−1)(2x−3)(x+2)4.
x=−1,x=3/2
Solve x+5x2−2x=1x2−2x+1x+5x2−2x=1x2−2x+1.
x=−1x=−1 or x=4
Find the vertical asymptotes of the function 4(x+2)(x+1)(3x+4)(2x−3)3(x−2)(x2−1)(2x−3)(x+2)44(x+2)(x+1)(3x+4)(2x−3)3(x−2)(x2−1)(2x−3)(x+2)4.
x=−2,x=1,x=2
Solve 1x−x3=−13x1x−x3=−13x.
x=−2x=−2 or x=2
The function f(x)=1x+3f(x)=1x+3 has a vertical asymptote at
x=−3
Find the holes of the function −2x(x+3)2(x+2)3x(x+2)(x+3)2−2x(x+3)2(x+2)3x(x+2)(x+3)2.
x=−3,x=−2,x=0
Find the vertical asymptotes of the function (x−1)(x−3)2(x+1)2(x−2)(x+2)(x−1)(x+3)(x−1)(x−3)2(x+1)2(x−2)(x+2)(x−1)(x+3).
x=−3,x=−2,x=2
What are the roots of f(x)=−3−2x−3−−−−−−−√f(x)=−3−2x−3?
x=−32
Solve x−5x2−1−1=−2xx−1x−5x2−1−1=−2xx−1.
x=−4
Solve x−62x+2x+12x=x2−x−6x2x−62x+2x+12x=x2−x−6x2.
x=−6x=−6 or x=−2/3
Simplify 3x2−3x3x2−33x2−3x3x2−3.
xx+1
What is the equivalent expression of x16y16x16y16?
xy−−√6
What is the equivalent expression of (xy)12(xy)12?
x√y√
What are the restricted values for 3xy24y÷2x23y3xy24y÷2x23y?
x≠0,y≠0
What are the restricted values for 6xyz2xy−y⋅2x2−7x+33xz−9z6xyz2xy−y⋅2x2−7x+33xz−9z?
x≠1/2,x≠3,y≠0,z≠0
What are the restricted values for x2−3x−2−4y⋅2x−2−xy2+2y2x2−3x−2−4y⋅2x−2−xy2+2y2?
x≠2,y≠0
Solve 7y−56y2−5y=3y+12y2−5y+1y7y−56y2−5y=3y+12y2−5y+1y.
y=21
The graph of y=x−−√y=x is translated 3 units to the left and 4 unitsdown. What is the equation of the graph that results from this translation?
y=x+3−−−−−√−4
Solve 1−y−1y=1y2+2y1−y−1y=1y2+2y.
y=−1
Simplify 12x2−6x−36−2x2+x+612x2−6x−36−2x2+x+6.
−6
Simplify −x2−x4x+2xx−x2−x4x+2xx.
−x+74
Simplify x2+x−62−xx2+x−62−x.
−x−3
Estimate the local maximum of y=2x3+x2−7x−6y=2x3+x2−7x−6.
(-1.25,0.41)
What is/are the xx-intercepts of the graph y=x4−2x3−11x2+12x+36y=x4−2x3−11x2+12x+36?
(-2,0), (3,0)
Estimate the local minimum of y=−x3−5x2−3x+9y=−x3−5x2−3x+9.
(-3,0)
What is/are the xx-intercepts of the graph y=−x6−6x5+50x3+45x2−108x−108y=−x6−6x5+50x3+45x2−108x−108?
(-3,0), (-1,0), (2,0)
What is/are the xx-intercepts of the graph y=−x3−5x2−3x+9y=−x3−5x2−3x+9?
(-3,0), (1,0)
What is the y-intercept of f(x)=2−x−−−√+2f(x)=2−x+2?
(0,2)
What is the yy-intercept of the graph y=−x3−5x2−3x+9y=−x3−5x2−3x+9?
(0,9)
What is the y-intercept of f(x)=4x+1−−−−−√−4f(x)=4x+1−4?
(0,−3)
Estimate the local minimum of y=2x3+x2−7x−6y=2x3+x2−7x−6.
(1,-10)
Find the lowest common multiple of x2+2x+1x2+2x+1 and x2−6x+9x2−6x+9.
(x+1)2(x−3)2
Find the lowest common multiple of x2−x−6x2−x−6 and x2+5x+6x2+5x+6.
(x+3)(x−3)(x+2)
Where does the graph of f(x)=4x+1−−−−−√−4f(x)=4x+1−4 start?
(−14,−4)
What is the range of f(x)=5xf(x)=5x?
(−∞,0)∪(0,∞(−∞,0)∪(0,∞)
What is the domain of f(x)=2−x−−−√+2f(x)=2−x+2?
(−∞,0]
What is the range of f(x)=−3−2x−3−−−−−−−√f(x)=−3−2x−3?
(−∞,0]
What is the range of f(x)=−4x+1f(x)=−4x+1?
(−∞,1)∪(1,∞(−∞,1)∪(1,∞)
What is the range of f(x)=−2x−2−2f(x)=−2x−2−2?
(−∞,−2)∪(−2,∞(−∞,−2)∪(−2,∞)
What is the domain of f(x)=1x+3f(x)=1x+3?
(−∞,−3)∪(−3,∞(−∞,−3)∪(−3,∞)
What is the domain of f(x)=−3−2x−3−−−−−−−√f(x)=−3−2x−3?
(−∞,−32]
Estimate the local maximum of y=−x6−6x5+50x3+45x2−108x−108y=−x6−6x5+50x3+45x2−108x−108.
--- (NOT: (2,0))
The minimum point on the graph of the equation y=f(x)y=f(x) is (−1,−3)(−1,−3). What is the minimum point on the graph of the equation y=f(x)+5y=f(x)+5?
--- (NOT: (−1,−8))
Find the value of (−64)23
--- (NOT: -16)
What transformation of the parent function f(x)f(x) is made to get f(x)−3f(x)−3?
--- (NOT: 3 units in the y-direction)
If the graph of f(x)f(x) is: Which of the following is the graph of −f(−x)−f(−x)?
--- (NOT: Arrow going from top left middle to bottom middle right)
If the graph of f(x)f(x) is: Which of the following is the graph of f(x−2)f(x−2)?
--- (NOT: Arrow pointing up towards the left)
Find the domain and range of the function −2x(x+3)2(x+2)3x(x+2)(x+3)2−2x(x+3)2(x+2)3x(x+2)(x+3)2.
--- (NOT: D:(−∞,−3)∪(−3,−2)∪(−2,0)∪(0,∞)D:(−∞,−3)∪(−3,−2)∪(−2,0)∪(0,∞) R:(−∞,0)∪(0,∞)R:(−∞,0)∪(0,∞))
Which of the following equations is an example of direct variation?I. f(x)=−xyzf(x)=−xyzII. f(x)=x3f(x)=x3III. f(x)=3x
--- (NOT: I only)
What transformation of the parent function f(x)f(x) is made to get f(3x)f(3x)?
--- (NOT: a vertical stretch by 3)
If the graph of f(x)f(x) is: Which of the following is the graph of −f(x)−f(x)?
--- (NOT: arrow from top left middle to bottom right middle)
What happens to the graph of y=x4−2x3−11x2+12x+36y=x4−2x3−11x2+12x+36 as xx heads toward ∞∞ and −∞−∞?
--- (NOT: as x→∞x→∞, y→−∞y→−∞ as x→−∞x→−∞, y→∞)
What is the lowest common denominator of 6−y3=y−446−y3=y−44?
12
What is the equivalent expression of x−1x−1?
1x
Which expression is equivalent to the given expression? 25-√3+35-√3−35-√3
25-√3
Simplify 4a2b32ab4a2b32ab.
2ab2
Simplify 3√3−6√33−6 by rationalizing the denominator.
3-√+2-√
What is the equivalent expression of (2x2y13)5(2x2y13)5?
32x10yy2−−√3
Evaluate 7C37C3.
35
Simplify 3x2−27x2+6x+9+2x−4x2+x−63x2−27x2+6x+9+2x−4x2+x−6.
3x−7x+3
The expression 150−−−√150 can be simplified to:
56-√
Write as a radical expression and evaluate if possible. 813
8-√3=2
Express the given radical in simplest form: 128−−−√
82-√
Find the value of (827)−23
94
If the graph of f(x)f(x) is: Which of the following is the graph of −f(x)−f(x)?
Arrow on right, pointing up
If the graph of f(x)f(x) is: Which of the following is the graph of f(x)−1f(x)−1?
Arrow pointing down in fourth quadrant
Find the domain and range of the function 4(x+2)(x+1)(3x+4)(2x−3)3(x−2)(x2−1)(2x−3)(x+2)44(x+2)(x+1)(3x+4)(2x−3)3(x−2)(x2−1)(2x−3)(x+2)4.
D:(−∞,−2)∪(−2,−1)∪(−1,1)∪(1,3/2)∪(3/2,2)∪(2,∞)D:(−∞,−2)∪(−2,−1)∪(−1,1)∪(1,3/2)∪(3/2,2)∪(2,∞) R:(−∞,∞)
Find the domain and range of the function (x−1)(x−3)2(x+1)2(x−2)(x+2)(x−1)(x+3)(x−1)(x−3)2(x+1)2(x−2)(x+2)(x−1)(x+3).
D:(−∞,−3)∪(−3,−2)∪(−2,1)∪(1,2)∪(2,∞)D:(−∞,−3)∪(−3,−2)∪(−2,1)∪(1,2)∪(2,∞) R:(−∞,∞)
Which of the following functions are discontinuous?I. f(x)=x−2x2+3x+2f(x)=x−2x2+3x+2II. f(x)=4x2+2x−62f(x)=4x2+2x−62III. f(x)=2x2+3x−1x+5
I and III only
Which expressions are equivalent to the given expression? 80√5√805I. 805−−√805II. 16−−√16III. 4
I, II, and III
Find the domain and range of the function −2x(x+3)2(x+2)3x(x+2)(x+3)2−2x(x+3)2(x+2)3x(x+2)(x+3)2.
--- (NOT: D:(−∞,−3)∪(−3,−2)∪(−2,0)∪(0,∞)D:(−∞,−3)∪(−3,−2)∪(−2,0)∪(0,∞) R:(−∞,0)∪(0,∞))
The graph of y=x−2−−−−√y=x−2 is is transformed to becomey=x−−√+5y=x+5. Which of the following statements best describes the effect this transformation has on the graph ofy=x−−√y=x?
--- (NOT: The graph is translated 5 units left and 2 units up.)
If the graph of f(x)f(x) is: Which of the following is the graph of f(x−2)f(x−2)?
--- (NOT: The graph right in the middle)
If the graph of f(x)=x2f(x)=x2, how will the graph be affected if the coefficient of x2x2 is changed to 1313?
--- (NOT: The parabola will be narrower)
If the graph of f(x)=x2f(x)=x2, how will the graph be affected if the coefficient of x2x2 is changed to 33?
--- (NOT: The parabola will be wider.)
What transformation of the parent function f(x)f(x) is made to get −2f(x)−2f(x)?
--- (NOT: a vertical stretch by 2)
The graph of y=x−−√y=x is reflected in the x-axis and then translated down 3 units. What is an equation that produces this transformation?
--- (NOT: y=−(x−−√−3))
Find the horizontal asymptote of the function −2x(x+3)2(x+2)3x(x+2)(x+3)2−2x(x+3)2(x+2)3x(x+2)(x+3)2.
--- (NOT: y=−2/3)
Simplify −5x−1x+2+2x−5x+2−5x−1x+2+2x−5x+2.
-3
What transformation of the parent function f(x)f(x) is made to get f(x)−3f(x)−3?
-3 units in the y-direction
Find the coefficient of fourth term of (4x−3)4(4x−3)4.
-432
Simplify x+1x2−1−x−1x2−2x+1x+1x2−1−x−1x2−2x+1.
0
Which expression is equivalent to the given expression? 22-√0⋅46-√
1630−−√
Simplify 6xyz2xy−y÷2x2−7x+33xz−9z6xyz2xy−y÷2x2−7x+33xz−9z.
18xz24x2−4x+1
What is the equivalent expression of (z−4312x3y14)−12(z−4312x3y14)−12?
2x3x−−√y√8z2−−√3
Simplify 6x22xy+8zxz6x22xy+8zxz.
3x2+8yxy
Simplify 6x22xy−8zxz6x22xy−8zxz.
3x2−8yxy
Simplify 3x2+3x−6x+23x2+3x−6x+2.
3x−3
Write as a radical expression and evaluate if possible. 8114
81−−√4=3
Find the lowest common multiple of 3xyz23xyz2 and 9x2y+9x29x2y+9x2.
9x2yz2(y+1)
Find the vertical asymptotes of the function (2x−1)(x+4)2(x−1)(3x+2)3x(x−4)(2x−1)3(2x−1)(x+4)2(x−1)(3x+2)3x(x−4)(2x−1)3.
x=0,x=1/2,x=4
Find the vertical asymptotes of the function (x+4)(x−1)(x−2)(x−2)2(x+4)(x+1)(x+4)(x−1)(x−2)(x−2)2(x+4)(x+1).
x=−1,x=2
Find the lowest common multiple of 2x+82x+8 and 2x−82x−8.
2(x+4)(x−4)
Simplify 235√32353 by rationalizing the denominator.
225√315
Find the coefficient of third term of (2x−1)6(2x−1)6.
240
Which expression is equivalent to the given expression? 180−−−√⋅42-√
2410−−√
Find the third term of (x2+2)4(x2+2)4.
24x4
What is 1414−−√÷72-√ in simplest form?
27-√
Simplify: 162-√3+243-√+142-√3+43-√
302-√3+283-√
Simplify 32√+15√−132+15−1 by rationalizing the denominator.
310√+32√+5√+14
Express the given radical in simplest form: 45−−√
35-√
Evaluate 9!.
362,880
Simplify 2x+3x+1+xx−12x+3x+1+xx−1.
3x2+2x−3x2−1
Simplify 3x2−27x2+6x+9−2x−4x2+x−63x2−27x2+6x+9−2x−4x2+x−6.
3x−11x+3
Find the lowest common multiple of 2x2−22x2−2 and 4x−44x−4.
4(x+1)(x−1)
Find the coefficient of third term of (x+2)5(x+2)5.
40
Evaluate 8C58C5.
56
Simplify x−6x−1⋅5x2−5xx−6x−6x−1⋅5x2−5xx−6.
5x
When 72−−√72 is expressed in simplest ab√ab form, what is the value of aa?
6
What is the equivalent expression of 3x13(2x−13−x43)3x13(2x−13−x43)?
6−3xx2−−√3
Evaluate 6!.
720
What happens to the graph of y=2x3+x2−7x−6y=2x3+x2−7x−6 as xx heads toward ∞∞ and −∞−∞?
--- (NOT: as x→∞x→∞, y→−∞y→−∞ as x→−∞x→−∞, y→∞)
What is the behavior of the graph y=−x6−6x5+50x3+45x2−108x−108y=−x6−6x5+50x3+45x2−108x−108 at each of its zeros?
--- (NOT: two resemble a quadratic function and one resembles a linear function)
What is the equivalent expression of x−23x−23?
--- (NOT: x2−−√3)
What is the lowest common denominator of 7y−56y2−5y=3y+12y2−5y+1y7y−56y2−5y=3y+12y2−5y+1y?
y2−5y
Find the horizontal asymptote of the function (x+4)(x−1)(x−2)(x−2)2(x+4)(x+1)(x+4)(x−1)(x−2)(x−2)2(x+4)(x+1).
y=0
The graph of y=x−−√y=x is translated 3 units to the right and slid 5 units up, what would be the resulting equation?
y=x−3−−−−−√+5
Solve 1y2=y−62y2+3y2+24y+48y21y2=y−62y2+3y2+24y+48y2.
y=−11/2y=−11/2 or y=−8/3
Solve 12y−16y2=−76y212y−16y2=−76y2.
y=−2
Find the fourth term of (2x−3y)7(2x−3y)7.
−15,120x4y3
Simplify 63√−12√+6√63−12+6 by rationalizing the denominator.
−76√−192√4
Simplify −3x2+6x18xy−3x2+6x18xy.
−x+26y
Expand (−x−3)5(−x−3)5.
−x5−15x4−90x3−270x2−405x−243