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

What is the lowest common denominator of 7y−56y2−5y=3y+12y2−5y+1y7y−56y2−5y=3y+12y2−5y+1y?

y2−5y

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)

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)

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

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-√

What is the equivalent expression of (z−4312x3y14)−12(z−4312x3y14)−12?

2x3x−−√y√8z2−−√3

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 6x22xy+8zxz6x22xy+8zxz.

3x2+8yxy

Simplify 6x22xy−8zxz6x22xy−8zxz.

3x2−8yxy

Simplify 3x2−27x2+6x+9−2x−4x2+x−63x2−27x2+6x+9−2x−4x2+x−6.

3x−11x+3

Simplify 3x2+3x−6x+23x2+3x−6x+2.

3x−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

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 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