Quiz about General Mathematics Reviewer

Question 1

Which of the following situation represents a one-to-one function?

Accepted Answer

The relation pairing a person to their fingerprint.

Answer

The relation pairing a book to its author.

Answer

The relation pairing the person to his/her citizenship.

Answer

The relation pairing a teacher to their classroom.

Question 2

Which of the following relationships do NOT represent one-to-one function?

Accepted Answer

Students to their subjects

Answer

Country to its capital city

Answer

Car to its license plate number

Answer

School to its School ID

Question 3

Which is NOT a one-to-one function?

Accepted Answer

$$f\left(x\right)=x^2$$

Answer

$$f\left(x\right)=x^3$$

Answer

$$f\left(x\right)=e^x$$

Answer

$$f\left(x\right)=2x$$

Question 4

Which of the following statements is FALSE?

Accepted Answer

The inverse of $$y=x$$ is $$y=\frac{1}{x}$$

Answer

A quadratic function is not a one-to-one function.

Answer

The inverse of $$f^{-1}\left(x\right)$$ is $$f\left(x\right)$$

Answer

The graph of the inverse function is a reflection of the graph of the original function along $$y=x$$

Question 5

Which of the following is the inverse of {(-4, 3), (-5, 2)}?

Accepted Answer

{(3, -4), (2, -5)}

Answer

{( -4, 3), (-5, 2)}

Answer

{(3, -4), (-2, 5)}

Answer

{(4, -3), (-5, 2)}

Question 6

The statement "A function has an inverse function if and only if it is one - to - one" is

Accepted Answer

always true

Answer

sometimes true

Answer

never true

Answer

false

Question 7

Which of the following is the correct representation of the inverse of the function given the table of values below?

Accepted Answer

Question 8

Which of the following is a graph of a one-to-one function?

Accepted Answer

Question 9

If 5 is a constant added to f(x) = 3x-2, what will its inverse be equal to?

Accepted Answer

$$f^{-1}\left(x\right)=\frac{x-3}{3}$$

Answer

$$f^{-1}\left(x\right)=3x+2$$

Answer

$$f^{-1}\left(x\right)=3x-2$$

Answer

$$f^{-1}\left(x\right)=\frac{x+2}{3}$$

Question 10

Which of the following is the graph of the inverse of the graph below?

Accepted Answer

Question 11

Determine the inverse of f(x) = 3x+5.

Accepted Answer

$$f^{-1}\left(x\right)=\frac{x-5}{3}$$

Answer

$$f^{-1}\left(x\right)=\frac{x+5}{3}$$

Answer

$$f^{-1}\left(x\right)=\frac{3x+5}{2}$$

Answer

$$f^{-1}\left(x\right)=\frac{x+5}{2}$$

Question 12

Find the inverse of $$f\left(x\right)=\frac{2x+3}{x-4}$$ .

Accepted Answer

$$f^{-1}\left(x\right)=\frac{4x+3}{x-2}$$

Answer

$$f^{-1}\left(x\right)=\frac{2x+3}{x+4}$$

Answer

$$f^{-1}\left(x\right)=\frac{x-4}{2x+3}$$

Answer

$$f^{-1}\left(x\right)=\frac{3x+2}{x-4}$$

Question 13

If $$f\left(x\right)=4x-1$$ , what is the inverse function $$f^{-1}\left(x\right)$$ ?

Accepted Answer

$$f^{-1}\left(x\right)=\frac{x+1}{4}$$

Answer

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

Answer

$$f^{-1}\left(x\right)=4x+1$$

Answer

$$f^{-1}\left(x\right)=4x-1$$

Question 14

Which of the following statements is TRUE regarding inverse functions?

Accepted Answer

The inverse of a one-to-one function is also one-to-one.

Answer

The graph of a function and its inverse are identical.

Answer

All functions have inverses.

Answer

The inverse of a function is always a function.

Question 15

One of these does not belong to the group, which one and why?

I. $$5^{\left(x+1\right)}=3^2$$ II. $$f\left(x\right)=5^{\left(x+1\right)}$$ III. $$4^{\left(-3x+5\right)}=16$$ IV. $$6=3\left(2\right)^{\left(3-x\right)}$$

Accepted Answer

II, because it is the only exponential function while the rest are all exponential equations.

Answer

I, because it is the only exponential equation while the rest are all exponential functions.

Answer

III, because it is the only exponential function while the rest are all exponential inequalities.

Answer

IV, because it is the only exponential equation while the rest are all exponential inequalities.

Question 16

Which of the following will result in the equation $$3^{\left(x+1\right)}\cdot27=9^{\left(x+2\right)}$$ ?

Accepted Answer

$$3^{\left(x+1\right)}\cdot3^3=3^{\left(2x+4\right)}$$

Answer

$$3^{\left(3x+3\right)}=3^{\left(2x+4\right)}$$

Answer

$$81^{\left(x+1\right)}=9^{\left(x+2\right)}$$

Answer

$$3^{\left(4x+4\right)}=3^{\left(2x+4\right)}$$

Question 17

Which two alternative solutions will solve the equation $$16^{\left(x+2\right)}\cdot4^3=2^{2x}$$ ?

I. $$4^{\left(2x+2\right)}\cdot4^3=4^x$$ II. $$4^{\left(2x+4\right)}\cdot4^3=4^x$$ III. $$4^{\left(2x+4\right)}\cdot2^6=4^x$$ IV. $$4^{\left(x+2\right)}\cdot2^6=4^x$$

Accepted Answer

II and III

Answer

I and III

Answer

I and IV

Answer

II and IV

Question 18

Which is being exemplified by $$27^{\left(x-2\right)}=9$$ ?

Accepted Answer

Exponential Equation

Answer

Exponential Expression

Answer

Exponential Function

Answer

Exponential Inequality

Question 19

Which of the following is an exponential inequality?

Accepted Answer

$$4^x>2^{\left(2x+1\right)}$$

Answer

$$2^{\left(2x+1\right)}$$

Answer

$$4^x=2^{\left(2x+1\right)}$$

Answer

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

Question 20

The teacher asks Joseph to solve the equation $$9^{\left(x-3\right)}=3^{\left(x-2\right)}$$ . What is the value of x?

Accepted Answer

4

Answer

-4

Answer

2

Answer

-2

Question 21

What should be considered in solving an exponential equation?

Accepted Answer

Bases on both sides must be the same.

Answer

Bases on both sides must be simplified.

Answer

Exponents on both sides must be the same.

Answer

Exponents on both sides must be simplified.

Question 22

What is the value of x in the equation $$8^x=16^{\left(x+5\right)}$$ ?

Accepted Answer

-20

Answer

20

Answer

-10

Answer

10

Question 23

Solve for the exponential equation $$3^x=3^2$$ ?

Accepted Answer

2

Answer

4

Answer

6

Answer

8

Question 24

A certain type of bacteria doubles its population every 15 minutes. If a sample of this bacteria is kept in ideal conditions and continues to double, how long will it take for the population to become eight times its original size?

Accepted Answer

45 mins

Answer

15 mins

Answer

30 mins

Answer

60 mins

Question 25

For an exponential function $$f\left(x\right)=b^x$$ , which can be a value of b?

Accepted Answer

2

Answer

-1

Answer

0

Answer

1

Question 26

A certain type of microorganism divides into two every 10 minutes. If you start with one microorganism, how many microorganisms will there be after 1 hour?

Accepted Answer

64

Answer

32

Answer

128

Answer

256

Question 27

What is the solution to $$2^{\left(x+3\right)}\ge4^{\left(x-1\right)}$$ ?

Accepted Answer

$$x\le5$$

Answer

$$x\ge5$$

Answer

$$x>5$$

Answer

$$x<5$$

Question 28

Solve for x: $$\left(\frac{1}{3}\right)^{\left(2x-2\right)}<\left(\frac{1}{27}\right)^{\left(x+1\right)}$$

Accepted Answer

$$x<-5$$

Answer

$$x>-5$$

Answer

$$x>5$$

Answer

$$x<5$$

Question 29

A company has 800 job applicants. During each round of interviews, half of the remaining applicants are eliminated. How many rounds of interviews are needed to reduce the number of applicants to 100?

Accepted Answer

3

Answer

2

Answer

4

Answer

5

Question 30

The solution to $$\log_39x^2-\log_3x=4$$ is x=9. 1. Which law of logarithms was used to solve it?

Accepted Answer

Quotient Law

Answer

Power Law

Answer

Product Law

Answer

Change of Base Formula

Question 31

Which of the following uses the laws /properties of logarithms to simplify $$\log_7x^2+\log_7x$$ ?

Accepted Answer

$$\log_7x^3$$

Answer

$$\log_7x$$

Answer

$$-\log_7x$$

Answer

$$-\log_7x^2$$

Question 32

John simplified $$\log_416+2\log_28$$ without using a calculator. Which laws were used?

A. C.

Accepted Answer

Power Law then Product Law

Answer

Product Law then Power Law

Answer

Quotient Law then Power Law

Answer

Power Law then Quotient Law

Question 33

Express $$\log_{25}5=\frac{1}{2}$$ into exponential form

Accepted Answer

$$25^{\frac{1}{2}}=5$$

Answer

$$\left(\frac{1}{2}\right)^5=25$$

Answer

$$25^5=\frac{1}{2}$$

Answer

$$\left(\frac{1}{2}\right)^{25}=5$$

Question 34

Which of the following is a logarithmic equation?

Accepted Answer

$$3=\log_7x$$

Answer

$$y=\log_4x$$

Answer

$$y\le\log_2x$$

Answer

$$y\ge\log_524$$

Question 35

What is the exponential form of the function $$y=\log_63x$$ ?

Accepted Answer

$$6^y=3x$$

Answer

$$6^{3x}=y$$

Answer

$$y^6=3x$$

Answer

$$y^{3x}=6$$

Question 36

If the formula for calculating the population is $$P=\log_{10}x$$ and x=100, what is the value of P?

Accepted Answer

3

Answer

2

Answer

10

Answer

1

Question 37

In the Grade 11 class of Miss Soto, Laura was asked to give an example of a logarithmic function. Which of the following examples should Laura give?

Accepted Answer

$$f\left(x\right)=\log_3\left(x+1\right)$$

Answer

$$\log\left(x+3\right)=\log4$$

Answer

$$\log\left(2x-1\right)>3$$

Answer

$$f\left(x\right)=x+4$$

Question 38

In Miss Alvarez's class, three students were asked to give examples of logarithmic functions, logarithmic equations, and logarithmic inequalities. Sarah cited $$f\left(x\right)=\log_2\left(x+6\right)$$ , Rachel cited $$\log_4\left(x-2\right)\ge1$$ , and Luis cited $$\log_5\left(3x-4\right)=2$$ . Who gave the correct example of a logarithmic equation?

Accepted Answer

Luis

Answer

Sarah and Luis

Answer

Sarah

Answer

Rachel

Question 39

Which of the following statement is TRUE?

Accepted Answer

$$\log_bx$$ can be negative if $$0

Answer

Common logarithms have base e.

Answer

Natural logarithms have base 10.

Answer

In the logarithmic form $$\log_bx,\ x$$ can be negative.

Question 40

Solve for x: $$\log_381=x$$

Accepted Answer

4

Answer

3

Answer

2

Answer

5

Question 41

The perimeter P of a regular hexagon is determined using the function $$P\left(x\right)=6x$$ , which function can be used to find the length of the side of the pentagon?

Accepted Answer

$$P^{-1}\left(x\right)=\frac{x}{6}$$

Answer

$$P^{-1}\left(x\right)=\frac{6}{x}$$

Answer

$$P^{-1}\left(x\right)=\frac{x+1}{6}$$

Answer

$$P^{-1}\left(x\right)=\frac{6-x}{x}$$

Question 42

What is $$\log_327$$ ?

Accepted Answer

3

Answer

1

Answer

2

Answer

5

Question 43

Solve for x: $$\log_4\left(x+2\right)=3$$

Accepted Answer

62

Answer

63

Answer

61

Answer

60

Question 44

Solve for x: $$\log_2\left(x+4\right)=5$$

Accepted Answer

28

Answer

16

Answer

25

Answer

31

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