Unit Test 7a: Rational Functions

Last updated about 3 years ago

17 questions

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Simplify \frac{8n}{n-3}+\frac{3n}{5n-6}

\frac{43n^{2}-9}{(5n-6)(n-3)}

\frac{8n+5n}{(n-3)+(5n-6)}

\frac{11n}{6n-9}

\frac{43n^{2}-57n}{(n-3)(5n-6)}

Subtract \frac{8}{x^{2}-x-2}-\frac{3}{x^{2}-4}

\frac{5x+1}{(x-2)(x+2)(x+1)}

\frac{5x+13}{(x-2)(x+2)(x+1)}

\frac{11x+19}{(x-2)(x+2)(x+1)}

\frac{5x+19}{(x-2)(x+2)(x+1)}

Simplify: \frac{1}{n+5}\cdot\frac{n^{2}+2n-15}{n-8}

\frac{n-3}{(n+5)(n-8)}

\frac{n^{2}+2n-14}{2n-3}

\frac{n-3}{n-8}

\frac{n^{2}+2n-15}{(n+5)(n-8)}

Solve for x: \frac{1}{x-8}+\frac{1}{x^{2}+x-72}=\frac{6}{x-8}

-\frac{44}{5}

-22

22

\frac{44}{5}

Solve for x:\frac{x}{2x-3}=\frac{3x}{x+11}

x={1,3}

x={0,4}

x={-4,0}

x={5,2}

Given the function f(x)=-\frac{2}{x-3}+5, identify the horizontal asymptote.. You do not need to show work for this one.

y=5

y=3

x=5

x=3

Graph f(x)=\frac{2}{x-1}-3. Label the asymptotes and two orded pairs on each branch.

Simplify \frac{m^{2}+m-30}{m^{2}+13m+42}\div\frac{m-2}{m+7}

\frac{m^{2}+2n-32}{m^{2}+14m+49}

\frac{-5}{2m^2}

\frac{m-5}{m-2}

\frac{(m-5)(n-2)}{(m-7)^2}

Forf(x)=\frac{-2x^2-2x}{x^2-3x-4} , what is the equation of the horizontal asymptote

There isn't one

y=0

y=-2

y=2

For f(x)=\frac{2x(x+1)}{(x-3)(x+1)}

, what are the coordinates of the holes, if it\they exist.

(-1,\frac{1}{2})

(-1,-2)

there isn't one

(-1,-\frac{1}{2})

For f(x)=\frac{2x(x+1)}{x^2-3x-4}
, what is the equation of the vertical asymptote

x=0

x=4

x=-1, x=4

x=-1

For f(x)=\frac{2x^{2}+2x}{x^2-2x-3}what is the Domain

x\neq\{3\}

x\neq\{3,-1\}

x\neq\{-1\}

x\neq\{3,1\}

Find the x-intercept, if one exists: f(x)=\frac{x^{2}+2x}{x^{2}+x}...I see that the option isn't here.. you will all get credit for this one....

(1,0),(-1,0)

(2,0)

(0,0)(1,0)

(-2,0)

What is the equation of the rational function graphed below:

What is the equation of the vertical asymptote? f(x)=\frac{4x^{2}+8x}{x+3}

x=3

x=-3

x=0

x=-2

Which statements are true for the given rational function. Select all that apply.

f(x)=\frac{x^{2}-6x}{x^2-4x-12}

The horizontal asymptote is at y=0.

There is a hole at (6,\frac{3}{4})

The vertical asymptote is at x=-2.

The x and y intercepts are at the origin.

The domain is all real numbers except -2.

Write an equation for the graph below:

\frac{x^{2}+x-2}{x+2}

\frac{x^{2}+x-2}{x-1}

\frac{1}{x-1}

\frac{x^{2}}{x^{2}-1}

Simplify \frac{8n}{n-3}+\frac{3n}{5n-6}

\frac{43n^{2}-9}{(5n-6)(n-3)}

\frac{8n+5n}{(n-3)+(5n-6)}

\frac{11n}{6n-9}

\frac{43n^{2}-57n}{(n-3)(5n-6)}

Subtract \frac{8}{x^{2}-x-2}-\frac{3}{x^{2}-4}

\frac{5x+1}{(x-2)(x+2)(x+1)}

\frac{5x+13}{(x-2)(x+2)(x+1)}

\frac{11x+19}{(x-2)(x+2)(x+1)}

\frac{5x+19}{(x-2)(x+2)(x+1)}

Simplify: \frac{1}{n+5}\cdot\frac{n^{2}+2n-15}{n-8}

\frac{n-3}{(n+5)(n-8)}

\frac{n^{2}+2n-14}{2n-3}

\frac{n-3}{n-8}

\frac{n^{2}+2n-15}{(n+5)(n-8)}

Solve for x: \frac{1}{x-8}+\frac{1}{x^{2}+x-72}=\frac{6}{x-8}

-\frac{44}{5}

-22

22

\frac{44}{5}

Solve for x:\frac{x}{2x-3}=\frac{3x}{x+11}

x={1,3}

x={0,4}

x={-4,0}

x={5,2}

Given the function f(x)=-\frac{2}{x-3}+5, identify the horizontal asymptote.. You do not need to show work for this one.

y=5

y=3

x=5

x=3

Simplify \frac{m^{2}+m-30}{m^{2}+13m+42}\div\frac{m-2}{m+7}

\frac{m^{2}+2n-32}{m^{2}+14m+49}

\frac{-5}{2m^2}

\frac{m-5}{m-2}

\frac{(m-5)(n-2)}{(m-7)^2}

Forf(x)=\frac{-2x^2-2x}{x^2-3x-4} , what is the equation of the horizontal asymptote

There isn't one

y=0

y=-2

y=2

For f(x)=\frac{2x(x+1)}{(x-3)(x+1)}
​
, what are the coordinates of the holes, if it\they exist.

(-1,\frac{1}{2})

(-1,-2)

there isn't one

(-1,-\frac{1}{2})

For f(x)=\frac{2x(x+1)}{x^2-3x-4}
, what is the equation of the vertical asymptote

x=0

x=4

x=-1, x=4

x=-1

 For  f(x)=\frac{2x^{2}+2x}{x^2-2x-3}what is the Domain

x\neq\{3\}

x\neq\{3,-1\}

x\neq\{-1\}

x\neq\{3,1\}

Find the x-intercept, if one exists: f(x)=\frac{x^{2}+2x}{x^{2}+x}...I see that the option isn't here.. you will all get credit for this one....

(1,0),(-1,0)

(2,0)

(0,0)(1,0)

(-2,0)

What is the equation of the rational function graphed below:

\frac{1}{x-2}

\frac{1}{x+2}

\frac{x}{x-2}

\frac{x^{2}}{x-2}

\frac{x}{x+2}

\frac{x^{2}}{x+2}

What is the equation of the vertical asymptote? f(x)=\frac{4x^{2}+8x}{x+3}

x=3

x=-3

x=0

x=-2

Which statements are true for the given rational function.  Select all that apply.

f(x)=\frac{x^{2}-6x}{x^2-4x-12}

The horizontal asymptote is at y=0.

There is a hole at (6,\frac{3}{4})

The vertical asymptote is at x=-2.

The x and y intercepts are at the origin.

The domain is all real numbers except -2.

   Write an equation for the graph below: 

\frac{x^{2}+x-2}{x+2}

\frac{x^{2}+x-2}{x-1}

\frac{1}{x-1}

\frac{x^{2}}{x^{2}-1}

Unit Test 7a: Rational Functions

Unit Test 7a: Rational Functions

Graph f(x)=\frac{2}{x-1}-3. Label the asymptotes and two orded pairs on each branch.

Simplify \frac{8n}{n-3}+\frac{3n}{5n-6}

Subtract \frac{8}{x^{2}-x-2}-\frac{3}{x^{2}-4}

Simplify: \frac{1}{n+5}\cdot\frac{n^{2}+2n-15}{n-8}

Solve for x: \frac{1}{x-8}+\frac{1}{x^{2}+x-72}=\frac{6}{x-8}

Solve for x:\frac{x}{2x-3}=\frac{3x}{x+11}

Given the function f(x)=-\frac{2}{x-3}+5, identify the horizontal asymptote.. You do not need to show work for this one.

Graph f(x)=\frac{2}{x-1}-3. Label the asymptotes and two orded pairs on each branch.

Simplify \frac{m^{2}+m-30}{m^{2}+13m+42}\div\frac{m-2}{m+7}

Forf(x)=\frac{-2x^2-2x}{x^2-3x-4} , what is the equation of the horizontal asymptote

For f(x)=\frac{2x(x+1)}{(x-3)(x+1)}​, what are the coordinates of the holes, if it\they exist.

For f(x)=\frac{2x(x+1)}{x^2-3x-4}, what is the equation of the vertical asymptote

For f(x)=\frac{2x^{2}+2x}{x^2-2x-3}what is the Domain

Find the x-intercept, if one exists: f(x)=\frac{x^{2}+2x}{x^{2}+x}...I see that the option isn't here.. you will all get credit for this one....

What is the equation of the rational function graphed below:

What is the equation of the vertical asymptote? f(x)=\frac{4x^{2}+8x}{x+3}

Which statements are true for the given rational function. Select all that apply.f(x)=\frac{x^{2}-6x}{x^2-4x-12}

Write an equation for the graph below:

For f(x)=\frac{2x(x+1)}{(x-3)(x+1)}

, what are the coordinates of the holes, if it\they exist.

For f(x)=\frac{2x(x+1)}{x^2-3x-4}
, what is the equation of the vertical asymptote

Which statements are true for the given rational function. Select all that apply.

f(x)=\frac{x^{2}-6x}{x^2-4x-12}