WorksheetsSimplifying Exponents & Rational Functions
Total questions: 152
Worksheet time: 13hrs 21mins
When you have a power to a power you __________________________________ the exponents.
Divide
Multiply
Add
Subtract
To turn a negative exponent positive you
______________________.
Multiplying
Change the negative to positive
Flip it
Adding
(2a2 b)(4ab2)
6a2b3
6a3b2
8a3b3
8a2b2
(2x2y3)2
22x4y5
2x4y5
4x2y5
4x4y6
−3c318c2
c6
−6c
c−6
−3c18
Simplify the expression
3x5y7−1
3x5y7
16x13y9
16x13y91
(m3m2n7)5
15m7n12
243m5n35
15m15n35
243m7n12
25x8y2
10x8y2
−10x2y6
25x2y8
x−10y−8x−2
y−8x8
x20y8
x8y8
x2x10y8
−8xy7
−32x2y10
32x10y2
16x2y10
What is the area of the rectangle with the given sides?
7x3y8z4
10x2y16z3
10x3y8z4
none of the above
23 = 8
42 = 16
32 × 333 =
(7-m)
(x2-49)/(x2+9x+14)
(x2+6x+8)/(x2-x-6)
Simplify
(8x + 32)/( x+4)
8/(x - 4)
-x/(x - 4)
-8
8
7 / (x - 3)
(2x2-98)/(2x2+18x+28)
Simplify: x4y15x8y12
y3x4
y3x12
x12y27
x4y3
Simplify: 20a5c45a3c10
a24c6
41a2c6
4a21c6
4c61a2
Simplify: (4w3y5)28w3y11
w32y
2w31y
w2y4
2w91y21
Simplify: 6x5y9−30x5y8
5y1
−5y
−5x10y17
y−5
Simplify: x2y−3x−4y7
x6y10
y10x6
x2y4
y4x2
Simplify: 8a−2c−324a3c4
16ac
3ac
3a5c7
a5c73
(x−2)(x+5)2x(x−2)
State the values of x which must be excluded to prevent division by zero.
-2 and 5
2 and -5
0, 2, and -5
0, -2, and 5
(x−4)(x+7)(x + 1)(x−4)
State the values of x that must be excluded to prevent division by zero.
-1, 4, and -7
-1 and 4
-4 and 7
4 and -7
x(x−3)(x−3)(x+4)
State the values of x that must be excluded to prevent division by zero.
0 and 3
0 and -3
3 and -4
0, 3, and -4
Simplify: x2−49x2+6x−7
x+7x−1
x+7x+1
x−7x−1
x−7x+1
Simplify: x2+3x−18x2+6x
x+3x
x−3x
x−3x+6
x+6x
Simplify: x2−4x2+7x+10
x+2x−5
x−2x−5
x+2x+5
x−2x+5
Simplify: x2−6x+5x2−25
x−1x+5
x−1x−5
x+1x+5
x+1x−5
Simplify: x2+4xx2+7x+12
x+4x+3
xx−3
xx+3
x2x+3
Simplify: x2−81x2−4x−45
x−9x+5
x+9x+5
x−9x−5
x+9x−5
State the excluded values.
4p+204
-5
-8/7
No excluded values
0, -3
State the excluded values.
4x−28x−7
1, -2
0,-2
9
7
State the excluded values.
a2+4a−21a+7
3, -7
9
9, 3
-5/2
Simplify the rational expression.
Simplify the rational expression.
Simplify the rational expression and state the excluded values.
Simplify the rational expression.
Simplify the rational expression.
Solve for x: 35−x2=x8
2
18/5
26/5
6
Solve the equation for x: x+22+x −25=x2−46
7
6
14
0
Solve for x: x−25+x2−2xx−6=x1
x = 5
x = 54
x = 1
x = - 4
Solve: x−22−x+11=x2−x−22
x = 2
x = -2
x = 6
x = 3
Solve 3xx−2=3x1+2
0
−53
-2
−51
Solve for y 3y+2−4y−1=32
y = -9
y = -3
y=1
y = 3
n−82n+16=2n−161−21
−523
7
−4
34
x2+8x+127x−49=x+63+x+21
−2
5
6
361
a+11=a2+a4a+12+a1
−413
−7, 1
−1
7
k+75=k+31+k2+10k+212k−2
2
1
−5
5
x+31=x+23−x2+5x+67
5
0
8
3
Solve for x
1/3
-5.5
5.5
2.5
Solve for x
4
2
-2
-4
Solve.
x = 5
x = -3
x = 3
x = -5
Solve.
x = 4.5
x = -4.5
x = 3
x = -3
3/5
3/4
1/4
4/5
2
1
-1
-4
Solve for x
x = 10
x = −1330
x = 6
no solution
Solve the equation for x.
x = 6
x = 12
x = 0
x = 3
Solve for x.
x = 2
x = 518
x = 526
x = 6
Solve and check for extraneous solutions
x= - 3 &x= -8
x= -3
No Solution
x= -8
m = 1
m = 31
m = 2
m = 32
Solve
No Solution
x = 6
x = 7
x = 5
How do you determine the vertical asymptote(s) of a rational function?
Calculate the average of the x-intercepts of the function.
Find the values of x that make the numerator of the function equal to zero.
Find the values of x that make the denominator of the function equal to zero.
Look for the x-values where the function is undefined.
What is the significance of a vertical asymptote in graphing rational functions?
It indicates the x-intercept of the function.
It represents the values where the function becomes undefined.
It represents the maximum value of the function.
It shows the points where the function is continuous.
What does a horizontal asymptote represent in the graph of a rational function?
It represents the average value of the function
It represents the behavior of the function as the input values become very large or very small.
It represents the x-intercept of the function
It represents the maximum value of the function
How do you find the slant asymptote(s) of a rational function?
Take the square root of the numerator to find the slant asymptote
Multiply the numerator by the denominator to find the slant asymptote
Subtract the denominator from the numerator to find the slant asymptote
Divide the numerator by the denominator using long division obtain the equation of the slant asymptote.
Find the domain of the rational function f(x)=x2−25x
State the end behavior asymptote:
x2−x2x2−5x+1
Determine the x-coordinate of the hole on the graph of
f(x)=x2+2x−3x2−2x+1
State the vertical asymptotes:
f(x)=2x2+3x−52
What is the slant asymptote of
f(x)=x−54x2+3x−9 ?
What are the horizontal and vertical asymptotes?
f(x)=x−13x+1
What are the x-intercept(s) for the function
f(x)=x−64x+12
f(x)= (x2-2x + 1)/(x2+2x - 3)
f(x) = 2 / (2x2+3x - 5)
Identify the point(s) of discontinuity.
f(x)=x−64
x = 0
x = 6
x = -6
x = 4
Identify the point(s) of discontinuity.
f(x)=(x−3)(x+2)x+2
Only x = 2
Only x = -2
Only x = 3
x = 2 and x = 3
x = -2 and x = 3
Identify the point(s) of discontinuity.
f(x)=3x2−3x−1
Only x = 1
Only x = -1
Only x = 3
x = -1 and x = 1
x = 1 and x = 3
Find and classify each discontinuity of the function.
f(x)=x+5xx = 5, vertical asympotoe
x = -5, hole
x = -5, vertical asymptote
continuous on the domain
Is there a hole or a vertical asymptote?
A hole when x = 2
A vertical asymptote at x = 2
there is no hole or vertical asymptote
Determine the removable point(s) of discontuity (or holes) for the following function.
f(x)=x2−9x+143x−6
x = 2
x = 7
x = 2 and x = 7
x = 0
Does Not Exist
Determine the vertical asymptote(s) for the following function.
f(x)=x−72x
x = 0
x = 2
x = 7
x = -7
Does Not Exist
Determine the vertical asymptote(s) for the following function.
f(x)=(x−5)(x+3)(x+3)
x = -3
x = 5
x = -3 and x = 5
x = 0
Does Not Exist
Determine the horizontal asymptote(s) for the following function.
f(x)=4x3−2x22x3+5x−1
y = 0
y = 2
y = 4
y = 1/2
Does Not Exist
Determine the horizontal asymptote(s) for the following function.
f(x)=x2−12x−5
y = 2
y = 1
y = -1
y = 0
Does Not Exist
Determine the horizontal asymptote(s) for the following function.
f(x)=x2−94x3
y = 4
y = 3
y = -3
y = 0
Does Not Exist
What is an asymptote?
an imaginary line that your function never touches
a part of your function
a point on your graph
a type of fruit
Determine all removable points of discontinuity (holes), vertical asympotes, and horizontal asympotes for the following function.
f(x)=2x2+5x−32x−1
Holes: x = -3
Vertical: x = 1/2
Horizontal: y = 0
Holes: x = 1/2
Vertical: x = -3
Horizontal: y = 0
Holes: Do Not Exist
Vertical: x = 1/2 and x = -4
Horizontal: y = 1
Holes: x = 1/2
Vertical: x = -3
Horizontal: y = 1
Holes: x = -3
Vertical: x = 1/2
Horizontal: Does Not Exist
