Free Printable ST#2_2223_GM_Rational Functions

1.

Given the function $f\left(x\right)=\frac{x-4}{x+2}$ , what is the y - intercept?

a)

$x=-2$

b)

$x=4$

c)

$y=1$

d)

$y=-2$

2.

Given the equation $\frac{9}{x+1}=\frac{2}{x^2-1}$ , what is the least common denominator?

a)

$x+1$

b)

$x-1$

c)

$x^2+1$

d)

$x^2-1$

3.

Given the rational equation $\frac{9}{x+1}=\frac{2}{x^2-1}$ , which solution is FALSE?

a)

$x+1\left(\frac{9}{x+1}=\frac{2}{x^2-1}\right)x^2-1$

b)

$x^2-1\left[\frac{9}{x+1}=\frac{2}{x^2-1}\right]x^2-1$

c)

$9\left(x^2-1\right)=2\left(x+1\right)$

d)

$9\left(x^2-1\right)-2\left(x+1\right)=0$

4.

Given the rational function $f\left(x\right)=\frac{x-4}{x+2}$ , what is the vertical asymptote?

a)

$x=-2$

b)

$x=4$

c)

$y=1$

d)

$y=-2$

5.

Given the rational function $f\left(x\right)=\frac{x-4}{x+2}$ , what is the horizontal asymptote?

a)

$x=-2$

b)

$x=4$

c)

$y=1$

d)

$y=-2$

6.

Given the rational function $f\left(x\right)=\frac{x-4}{x+2}$ , what is the x - intercept?

a)

$x=-2$

b)

$x=4$

c)

$y=1$

d)

$y=-2$

7.

Luis and Berto are renovating their treehouse. Luis did the first coating for 4 hours. Berto did the second coating. Together, they painted it for 2.4 hours. Find the number of hours Berth took to do the second coating. What is the working equation?

a)

$\frac{1}{4}+\frac{1}{x}=\frac{1}{2.4}$

b)

$\frac{1}{4}+\frac{1}{x}=2.4$

c)

$4+x=2.4$

d)

$\frac{1}{4}+\frac{1}{2.4}=\frac{1}{x}$

8.

Luis and Berto are renovating their treehouse. Luis did the first coating for 4 hours. Berto did the second coating. Together, they painted it for 2.4 hours. Find the number of hours Berto took to do the second coating.

a)

$3\ hrs$

b)

$3.5\ hrs$

c)

$4\ hrs$

d)

$6\ hrs$

9.

Solve for x $\frac{9}{x+1}=\frac{2}{x^2-1}$ . Which of the following solution/s is/are TRUE? $i.\ 9x^2+2x\ -\ 11=0,\ \left(9x-11\right)\left(x+1\right)=0,\ x\ =\ \frac{11}{9},\ x=-1$

$ii.\ 9\left(x^2-1\right)=2\left(x+1\right);\ 9x^2-2x-10\ =\ 0,\ \left(3x-5\right)\left(3x+2\right);\ x=\frac{5}{3},\ x=\frac{-3}{2}$ $iii.\ 9x^2-2x-7=0;\ \left(9x+7\right)\left(x-1\right)=0,\ x\ =\ 1,\ x=\frac{-7}{9}$ $iv.\ \ 9x^2-2x-11=0\ ;\ \left(9x\ -11\right)\left(x+1\right)=0;\ x=\frac{11}{9},\ x\ =\ -1$

a)

i only

b)

iv only

c)

both i and iv

d)

ii. only

10.

Given the function $f\left(x\right)=\frac{3}{4-2x}$ , what is the restriction of x?

a)

$-4$

b)

$-2$

c)

$2$

d)

$4$

11.

Given the function $f\left(x\right)=\frac{4}{\left(x-2\right)\left(x+3\right)}$ , what are the restricted values of x?

a)

$2\ and\ -3$

b)

$2\ and\ 3$

c)

$-2\ and\ 3$

d)

$-2\ and\ -3$

12.

Which is always TRUE about $R\left(x\right)=\frac{P\left(x\right)}{Q\left(x\right)}$ ?

a)

$P\left(x\right)=0$

b)

$P\left(x\right)\ne0$

c)

$Q\left(x\right)=0$

d)

$Q\left(x\right)\ne0$

13.

Which of the following are paired correctly? $I.\ Rational\ Function\ \ \ \ \ \ \ \ \ \ i.\ \frac{2}{x}=3+x$ $II.\ Rational\ equation\ \ \ \ \ \ \ \ ii.\ \frac{x+4}{x+5}$ $III.\ Rational\ Expression\ \ \ \ \ iii.\ y=\frac{1}{x-6}$

a)

I: iii and II:i only

b)

I:iii and III: I only

c)

II: I and III: ii only

d)

I:iii , II:i and III: ii

14.

Given the rational equation $\frac{x+1}{x-2}=\frac{1}{x+2}+1$ , which can be multiplied to remove all the denominators?

a)

$x-2$

b)

$x+2$

c)

$x^2-4$

d)

$x+1$

15.

When you solved the rational equation and got x = 5 as your answer , then the solution $\frac{1}{x-5}+...=...\ ,\$

a)

extraneous

b)

imaginary

c)

correct

d)

undefined

16.

Given the rational inequality $\frac{x+2}{x+3}\ge0\$ , what is TRUE about the rational expression $\frac{x+2}{x+3}$ ?

a)

positive

b)

negative

c)

zero

d)

positive or zero

17.

Given the rational inequality, and the table of signs, what should be the signs in the question marks ?

a)

$+\ ,\ -\$

b)

$-\ ,\ +$

c)

$+\ ,\ +$

d)

$-\ ,\ -\$

18.

Which intervals satisfy the inequality? COPY THE TABLE AND COMPLETE THE SOLUTION. Upload your solution paper in our google classroom ( 2 points )

a)

$\left(-\infty,\ -4\right)$

b)

$\left(-\infty,-4\right]\cup\left(5,\infty\right)$

c)

$\left[-4,5\right)$

d)

$\left(-\infty,-4\right)\cup\left(5,\infty\right)$

19.

Solve the inequality $\frac{\left(x-2\right)\left(x+1\right)}{x+3}<0$ using the table of signs. SHOW YOUR COMPLETE SOLUTION and upload it in the google classroom ( 4 points)

a)

$\left(-\infty,-3\right)\cup\left[-1,2\right]$

b)

$\left(-\infty,-3\right)\cup\left(-1,2\right)$

c)

$\left(-\infty,-3\right]\cup\left(-1,2\right)$

d)

$\left(-\infty,-3\right]\cup\left[-1,2\right]$

20.

Given the rational expression $R\left(x\right)=\frac{P\left(x\right)}{Q\left(x\right)}$ , when the degrees of P(x) and Q(x) are the same , then ______

a)

it's horizontal asymptote is the ratio of their leading coefficients

b)

it's horizontal asymptote is the x - axis or y = 0

c)

there is an oblique asymptote

d)

there is no horizontal asymptote

21.

What is the inverse of the function $f\left(x\right)=9\ -\ 2x$ ?

a)

$f^{-1}\left(x\right)=\frac{9-x}{2}$

b)

$f^{-1}\left(x\right)=\frac{x-9}{2}$

c)

$f^{-1}\left(x\right)=\frac{x+9}{2}$

d)

$f^{-1}\left(x\right)=\frac{x-2}{9}$

22.

Which of the graphs is TRUE about an inverse function?

a)

b)

c)

d)

23.

Given a rational function $g\left(x\right)=\frac{4}{x-5}$ , what are the asymptotes?

a)

$x\ =-\ 5\ and\ y\ =\ 0$

b)

$x\ =\ 5\ \ and\ y\ =\ 0\$

c)

$x\ =\ 5\ and\ y\ =\ 4$

d)

$x\ =\ -5\ and\ y\ =\ 4$

24.

What are the x and y - intercepts of the function $h\left(x\right)=\frac{x+1}{x-2}$ ?

a)

x - intercept = 2, y - intercept = -0.5

b)

x - intercept = -1 y -intercept = - 0.5

c)

x-intercept = - 0.5 y- intercept = 2

d)

x-intercept = - 0.5 y - intercept = - 1

25.

Which of the given graphs represent the function $f\left(x\right)=\frac{x+1}{x-2}$ ?

a)

b)

c)

d)

26.

Which of the situations does NOT represent one - to - one function?

a)

students. to identification numbers

b)

face mask to a person

c)

concert tickets to seat number

d)

Bosconian to Don Bosco Schools

27.

Given the function $f\left(x\right)=\frac{2x+3}{x+5}$ $I.\ The\ vertical\ asymptote\ is\ x\ =\ -5$ $II.\ The\ horizontal\ asymptote\ is\ y\ =\ 2$

a)

Only statement In is true.

b)

Only statement II is true.

c)

Both statements are true.

d)

Both statements are false

28.

Given the function $f\left(x\right)=\frac{x^2+4x}{x-2}$ , $I.\ The\ vertical\ asymptote\ is\ x\ =\ -2$ $II.\ The\ horizontal\ asymptote\ is\ y\ =\ 1$

a)

Only statement I is true.

b)

Only statement II is true.

c)

Both statements are true.

d)

Both statements are false.

29.

Given the function $f\left(x\right)=\frac{1}{x^2+2x+1}$ . $I.\ The\ vertical\ asymptote\ is\ x\ =\ 1$ $II.\ The\ horizontal\ asymptote\ is\ y\ =\ 0$

a)

Only statement I is true.

b)

Only statement II is true

c)

Both statements are true.

d)

Both statements are false.

ST#2_2223_GM_Rational Functions

Total questions: 29

Worksheet time: 1hrs 12mins

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