Quiz about Quiz 5 & 6

Question 1

If a function is transformed, what kind of shift happens with this function:

$$f\left(x\right)=2^x+3$$

Accepted Answer

Vertical

Answer

Undefined

Answer

Horizontal

Answer

Zero

Question 2

Given this function, how many units will the function shift?

$$f\left(x\right)=2^x+3$$

Accepted Answer

up 3

Answer

right 1

Answer

left 2

Answer

down 4

Question 3

If a function is transformed, what kind of shift happens with this function:

$$f\left(x\right)=2^{\left(x-4\right)}$$

Accepted Answer

Horizontal

Answer

Undefined

Answer

Vertical

Answer

Zero

Question 4

Given this function, how many units will the function shift?

$$f\left(x\right)=2^{\left(x-4\right)}$$

Accepted Answer

shift 4

Answer

shift 2

Answer

shift 1

Answer

shift 8

Question 5

Given this function, which direction will the function shift?

$$f\left(x\right)=2^{\left(x-4\right)}$$

Accepted Answer

right

Answer

left

Question 6

If $$f\left(x\right)\ =\ 2^x$$ is stretched by a factor of 4, then point (0,1) becomes what ordered pair?

Accepted Answer

(0,4)

Answer

(2,4)

Answer

(3,6)

Answer

(4,8)

Question 7

If $$f\left(x\right)\ =\ 2^x$$ is compressed by half its height, then point (1,2) becomes what ordered pair?

Accepted Answer

(1,1)

Answer

(1,2)

Answer

(0,1)

Answer

(2,4)

Question 8

If this point is reflected about or across the y-axis, what are the coordinates or the ordered pair for the new point?

Accepted Answer

(-1,2)

Answer

(1,-2)

Answer

(1,2)

Answer

(-1,-2)

Question 9

If this point is reflected about or across the x-axis, what are the coordinates or the ordered pair for the new point?

Accepted Answer

(1,-2)

Answer

(1,2)

Answer

(-1,2)

Answer

(-1,-2)

Question 10

Simplify:

$$5^{10} imes5^2$$

Accepted Answer

$$5^{12}$$

Answer

$$10^{12}$$

Answer

$$25^{12}$$

Question 11

Simplify:

$$3^4 imes3^8$$

Accepted Answer

$$3^{12}$$

Answer

$$9^{12}$$

Answer

$$6^{12}$$

Question 12

Simplify:

$$\frac{a^{12}}{a^3}$$

Accepted Answer

$$a^9$$

Answer

$$a^{15}$$

Question 13

Simplify:

$$\frac{c^{15}}{a^3}$$

Accepted Answer

$$c^{12}$$

Answer

$$c^{18}$$

Question 14

Simplify:

$$\left(w^3\right)^2$$

Accepted Answer

$$w^6$$

Answer

$$w^{32}$$

Answer

$$w^5$$

Question 15

Simplify:

$$\left(a^2b^3\right)^5$$

Accepted Answer

$$a^{10}b^{15}$$

Answer

$$a^7b^8$$

Answer

$$a^{25}b^{35}$$

Question 16

Simplify completely:

$$\frac{18x^3y^{-2}z^0}{3x^{-5}y^7}$$

Accepted Answer

$$\frac{6x^8}{y^9}$$

Answer

$$\frac{15y^5}{x^2}$$

Answer

$$21x^8y^9$$

Question 17

Simplify completely:

$$\left(\frac{2x^{-4}yz^2}{4x^3y^{-5}z^2}\right)^{-2}$$

Accepted Answer

$$\frac{4x^{14}}{y^{12}}$$

Answer

$$\frac{y^6}{2x^7}$$

Answer

$$\frac{y^{10}z^2}{16x^2}$$

Answer

$$\frac{x^2y^8z^0}{4}$$

Question 18

What are the steps for solving this equation?

$$3^{\left(x+1\right)}=\ \frac{1}{9}$$

Accepted Answer

Step 1: The base is $$3^2$$

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

Accepted Answer

Step 2: The negative should be $$3^{-2}$$ .

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

Accepted Answer

Step 3: X = -3

$$x+1=-2$$

Answer

Step 1: The base is 9

Question 19

What should you do when you need to find the INTERSECTION POINT of two functions?

Accepted Answer

Set them equal to each other.

Answer

Get the same base on each side.

Answer

Make each of them zero.

Answer

Guess and check

Question 20

What is the intersection point of these two functions:

$$f\left(x\right)\ =\ 6\left(3x\right)$$ and $$g\left(x\right)\ =\ 18\left(3^{\left(-x+1\right)}\right)$$

Accepted Answer

(1,18)

Answer

(1,6)

Answer

(3,1)

Answer

(2,9)

Question 21

What step should you do to find the INVERSE of a function?

Accepted Answer

switch x and y places

Answer

Solve for x

Answer

Solve for y

Answer

Substitute exponents instead of logorithms.

Question 22

What step is my first in finding the inverse of this function:

$$f\left(x\right)=5^x+1$$

Accepted Answer

$$x=5^y+1$$

Answer

$$y\ =5^x+1$$

Question 23

Solve for y

$$x=5^y+1$$

Accepted Answer

$$\log_5\left(x-1\right)=y$$

Answer

$$x-1=5^y$$

Question 24

What is the inverse of $$f\left(x\right)=5^x+1$$ ?

Accepted Answer

$$f^{-1}\left(x\right)=\log_5\left(x-1\right)$$

Answer

$$f^{-1}\left(x\right)=\log_5\left(x\right)+1$$

Answer

$$f^{-1}\left(x\right)=\log_5\left(x\right)-1$$

Answer

$$f^{-1}\left(x\right)=\log_5\left(x+1\right)$$

Question 25

How can you change the LOGARITHMIC FORM into EXPONENT FORM?

$$\log_bx=y$$ becomes ?

Accepted Answer

$$b^y=x$$

Answer

$$\log_bx=y$$

Answer

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

Question 26

Using the exponent form, solve for x:

Exponent form: $$b^y=x$$ Solve for: $$\log_327\ =\ x$$

Accepted Answer

x=3

Answer

x=4

Answer

x=0

Answer

x=16

Question 27

Using the exponent form, solve for x:

Exponent form: $$b^y=x$$ Solve for: $$\log_4\left(\frac{1}{16}\right)\ =\ x$$

Accepted Answer

x=-2

Answer

x=3

Answer

x=4

Answer

x=0

Question 28

Using the exponent form, solve for x:

Exponent form: $$b^y=x$$ Solve for: $$\log_71\ =\ x$$

Accepted Answer

x=0

Answer

x=3

Answer

x=4

Answer

x=-2

Question 29

Using the exponent form, solve for x:

Exponent form: $$b^y=x$$ Solve for: $$\log_2x\ =\ 4$$

Accepted Answer

x=16

Answer

x=4

Answer

x=0

Answer

x=-2

Question 30

Using the exponent form, solve for x:

Exponent form: $$b^y=x$$ Solve for: $$\log_x81\ =\ 4$$

Accepted Answer

x=3

Answer

x=16

Answer

x=0

Answer

x=-2

Question 31

What other equation helps with vertical asymptotes?

$$f\left(x\right)=\log_2\left(x\right)$$ goes to __________?

Accepted Answer

$$f\left(x\right)=\log_b\left(x-h\right)+k$$

Answer

$$f\left(x\right)=\log_y\left(b+h\right)-k$$

Question 32

What is the inverse function of $$f\left(x\right)=2\log_5\left(x+3\right)-7$$ ?

Accepted Answer

$$f^{-1}\left(x\right)=5^{\frac{1}{2}\left(x+7\right)}-3$$

Answer

$$f^{-1}\left(x\right)=\frac{5^{\left(z+7\right)}}{2}-3$$

Answer

$$f^{-1}\left(x\right)=2\left(5^{\left(x-3\right)}\right)-7$$

Answer

$$f^{-1}\left(x\right)=\frac{1}{2}5^{\left(x-3\right)}+7$$

Question 33

Expand this equation:

$$\log_2\ \frac{x^2y}{z}$$

Accepted Answer

$$2\log_2x+\log_2y-\log_2z$$

Answer

$$\log_2\left(x^2+y\right)-\log_2z$$

Answer

$$\log_2\left(x^2+y\right)-z$$

Answer

$$\log_22x+\log_2y-\log_2z$$

Question 34

Using the Power Rule of Logs $$\left(\log_bx^c=c\log_bx\right)$$ , combine this equation:

$$2\log_36-\log_34=$$

Accepted Answer

2

Answer

4

Answer

8

Answer

12

Question 35

What power of 10 solves for x? Hint: use $$b^y=x$$

$$\log1000=$$

Accepted Answer

$$10^y=1000$$

y=3

Answer

10y=1000

y=100

Question 36

What power of 10 solves for x? Hint: use $$b^y=x$$

$$\log\ \frac{1}{100}=$$

Accepted Answer

$$10^y=\frac{1}{100}$$

y=-2

Answer

10y=100

y=-10

Question 37

What number is $$\ln\left(e\right)=$$ ?

Accepted Answer

1

Answer

0

Answer

2

Answer

3

Question 38

What number is $$\ln\left(1\right)=$$ ?

Accepted Answer

0

Answer

1

Answer

2

Answer

3

Question 39

What number is $$\ln\left(\frac{1}{e}\right)=$$ ?

Accepted Answer

-1

Answer

0

Answer

2

Answer

7

Question 40

When solving for x in this equation $$\log_2\left(x+1\right)=3$$ , should you set up the problem using $$b^y=x$$ ?

Accepted Answer

Yes

Answer

No

Question 41

Solve for x in this equation

$$\log_2\left(x+1\right)=3$$

Accepted Answer

x=7

Answer

x=2

Answer

x=5

Answer

x=6

Question 42

Use this formula to solve for x: $$\log_b\left(x\right)+\log_b\left(y\right)=\log_b\left(xy\right)$$

$$\log_6\left(x-5\right)+\log_6x=1$$

Accepted Answer

x=6

Answer

x=1

Answer

x=3

Answer

x=5

Question 43

Exponential functions are "1-to-1" functions, but logarithmic functions are not.

Accepted Answer

False

Answer

True

Quiz 5 & 6

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