algebra 2b - unit 1: exponential and logarithmic functions, part 1

what is the initial value of the function?

-3

what is the intial value of the function f(x) = 9(2/3)^x + 4?

13

which graph shows f(x) = 3^x+4 and the translation g(x) = f(x - 5)?

https://cdstools.flipswitch.com/asset/media/1239881

lesson 3

inverse functions

what is the exponential form of x = log_5 y/2?

y = 2 * 5^x

the function that represents the depreciation value of rhonda's car is c(t) = 25,000(0.751)^t what was the initial value of rhonda's car at the moment she bought it?

$25,000

what is the closest approximate value of ln(0.9)?

-0.1

what is the closest approximate value of ln(0.4)?

-0.9

the graph shows preimage f(x) and image g(x) = f(x - h) https://cdstools.flipswitch.com/asset/media/1239930 what is the value of h?

-4

what is the horizontal asymptote of the function f(x) = 2^x - 5?

-5

what is the closest approximate value of log 3.7?

0.6

the graph shows preimage f(x) and image g(x) = f(1/bx). https://cdstools.flipswitch.com/asset/media/1239907 what is the value of b?

1/2

hot tea is cooling in a room that has a temperature of 72 fahrenheit. the equation that represents this model is f(x) = 109(0.935)^t + 72, where t represents the number of minutes that pass. what was the starting temperature of the tea?

181

which equation is equivalent to 7^2 = 49?

2 = log_7 49

what is the closest approximate value of ln(7.4)?

2.0

what is the closest approximate value of log 250?

2.4

what is the closest approximate value of log_3 15?

2.5

when finding the inverse of 27^3, what is the base of the logarithm?

27

what is the closest approximate value of ln(20)?

3

what is the value of log_2 8?

3

what is the closest approximate value of log_7 610?

3.3

when finding the inverse of 36^2, what is the base of the logarithm?

36

what is the exponential form of m = log_3 (34 − n)?

3^m + n = 34

examine the graph. decreasing exponential graph with points (0, 4), (-2, 7), (-3, 11) what is the initial value of the function?

4

the graph shows preimage f(x) and image g(x) = af(x). https://cdstools.flipswitch.com/asset/media/1239931 what is the value of a?

4

what is the value of log 10,000?

4

what is the value of log_3 81?

4

what is the exponential form of log_4 1,024 = 5?

4^5 = 1,024

what is the exponential form of log_4 64 = x?

4^x = 64

what is the value of log 100,000

5

the graph shows preimage f(x) and image g(x) = f(x) + k https://cdstools.flipswitch.com/asset/media/1239908 what is the value of k?

6

what is the exponential form of log_6 216 = 3?

6^3 = 216

when finding the inverse of 7^5, what is the base of the logarithm?

7

when finding the inverse of 8^4, what is the base of the logarithm?

8

which statement correctly describes the end behavior of the function?

as x approaches -inf, f(x) approaches 3, and x approaches inf, f(x) approaches inf.

what is the domain and range of the function? (0, -3), ( 1, -2), (2, 0), (3, 4)

domain: (-inf, inf) range: (-4, inf)

lesson 5

evaluating logarithms

lesson 1

exponential functions

suppose james has a credit card with a balance of $4,289. each month, the credit card company charges 5% interest. james pays off all new purchases that he makes each month without paying off the old balance of its interest. he wants to know what the balance on his credit card will be one year from now. is this situation an example of exponential growth or exponential decay?

exponential growth

which function will have a graph that decreases?

f(x) = 1.25(0.3)^x + 7

which function will have a graph that increases?

f(x) = 2(4)^x + 6

which function has a horizontal asymptote equal to 2?

f(x) = 4 * 3^x + 2

the function f(x) = 3^x is dilated to become g(x) = 1/2 * 3^x. what is the effect on f(x)?

f(x) is compressed vertically by a factor of 1/2

the function f(x) = 2^x is transformed to become g(x) = 2^-x. what is the effect on f(x)?

f(x) is reflected over the y-axis

the function f(x) = 5^x is dilated to become g(x) = 5 1/4^x. what is the effect on f(x)?

f(x) is stretched horizontally by a factor of 4

the function f(x) = 5^x is dilated to become g(x) = 3 * 5^x. what is the effect on f(x)?

f(x) is stretched vertically by a factor of 3

a function is translated from f(x) = 2^x to get g(x) = 2^x-3. what is the effect on f(x)?

f(x) moves 3 units to the right

a function is translated from f(x) = 2 * 3^x + 4 to g(x) = 2 * 3^x - 1. what is the effect on f(x)?

f(x) moves 5 units downward

what is the inverse of f(x) = √4x - 1?

f^-1(x) = (x+1)^2/4

what is the inverse of f(x) = 3/x+1?

f^-1(x) = 3/x - 1

what is the inverse of f(x) = 5/x+2 - 4?

f^-1(x) = 5/x+4 - 2

what is the inverse of f(x) = 3x-5/7?

f^-1(x) = 7x+5/3

given f(x) = 10^x + 1, what is f^-1(x)?

f^-1(x) = log(x - 1)

given f(x) = 2^x, what is f^-1(x)?

f^-1(x) = log_2 (x)

given f(x) = 3^x - 2, what is f^-1(x)?

f^-1(x) = log_3 (x + 2)

given f(x) = 5^x, what is f^-1(x)?

f^-1(x) = log_5 x

what is the inverse of f(x) = 4x/5 - 13?

f^1(x) = 5x/4 + 65/4

the graph shows a transformation of the preimage f(x) = 2^x - 1 to become g(x). https://cdstools.flipswitch.com/asset/media/1239911 what is the transformation rule and what is the function rule for g(x)?

g(x) = -3f(x) g(x) = -3(2^x) + 3

the graph shows a reflection of the preimage f(x) = 2^x + 3 to become g(x). https://cdstools.flipswitch.com/asset/media/1239910 what is the transformation rule and what is the function rule for g(x)?

g(x) = -f(x) g(x) = -2^x - 3

the graph shows a translation of the preimage f(x) = 2^x + 1 to become g(x). https://cdstools.flipswitch.com/asset/media/1239908 what is the transformation rule and what is the function rule for g(x)?

g(x) = 2^x - 3 g(x) = f(x) - 4

the graph shows a dilation of the preimage f(x) = 2^x + 3 to become g(x). https://cdstools.flipswitch.com/asset/media/1239933 what is the transformation rule and what is the function rule for g(x)?

g(x) = 3f(x) g(x) = 3 * 2^x + 9

the graph shows a translation of the preimage f(x) = 2^x - 1 to become g(x). https://cdstools.flipswitch.com/asset/media/1239932 what is the transformation rule and what is the function rule for g(x)?

g(x) = f(-3x) g(x) = 2^-3x - 1

the graph shows a dilation of the preimage f(x) = 2^x - 1 to become g(x). https://cdstools.flipswitch.com/asset/media/1239912 what is the transformation rule and what is the function rule for g(x)?

g(x) = f(1/2x) g(x) = 2^1/2x - 1

a city zoo decided to start a new exhibit for prairie dogs. when the exhibit opened, they had 2 prairie dogs. since then, the population of prairie dogs has tripled each year. this can be represented by the exponential function f(x) = 2 * 3^x. which graph shows the increasing population of prairie dogs?

graph with points (0, 2), (1, 6), (2, 18)

which graph shows f(x) = 4 * 2^x+1 + 3 and its translation g(x) = f(x) - 5?

https://cdstools.flipswitch.com/asset/media/1238825

which graph shows f(x) = 2^x+3 + 5 and its translation g(x) = 2^x-1 + 5?

https://cdstools.flipswitch.com/asset/media/1238833

which graph shows f(x) = 4^x-3 - 2 and its translation g(x) = 4^x+1 - 2?

https://cdstools.flipswitch.com/asset/media/1239886

which graph shows f(x) = 2^x + 1 and the dilation g(x) = 3f(x)?

https://cdstools.flipswitch.com/asset/media/1239890

which graph shows f(x) = 4^x - 2 and the dilation g(x) = f(6x)?

https://cdstools.flipswitch.com/asset/media/1239894

which graph shows f(x) = 2^x + 2 and the dilation g(x) = 2^1/5x + 2?

https://cdstools.flipswitch.com/asset/media/1239898

which graph shows f(x) = 3^x - 2 and the transformation g(x) = -f(x)?

https://cdstools.flipswitch.com/asset/media/1239902

which graph shows f(x) = 3 * 2^x-7 + 3 and its translation g(x) = f(x + 7)?

https://cdstools.flipswitch.com/asset/media/1239913

which graph shows f(x) = 3 * 2^x - 2 and its translation g(x) = 3 * 2^x + 3?

https://cdstools.flipswitch.com/asset/media/1239918

which graph shows f(x) = 2^x + 2, and the transformation g(x) = 2^-x + 2?

https://cdstools.flipswitch.com/asset/media/1239922

which graph shows f(x) = 2^x + 2 and the dilation g(x) = 1/3(2^x + 2)?

https://cdstools.flipswitch.com/asset/media/1239926

which equation is equivalent to 2^3 = 8?

log_2 8 = 3

which equation is equivalent to 3 ⋅ 2^3 = 24?

log_2 8 = 3

which equation is equivalent to 4^2 = 16?

log_4 16 = 2

which equation is equivalent to 4^3 = 64?

log_4 64 = 3

lesson 4

logarithms

which equation is equivalent to ℓ^m = n?

m = log_ ℓ n

which equation is equivalent to p^q = r?

q = log_p r

what is the domain and range of the function f(x) = 3(1/3)^x - 1?

range: (-1, inf) domain: (-inf, inf)

examine the graph. decreasing exponential graph with points (0, 4), (-2, 7), (-3, 11) what is the domain and range of the function?

range: (3, inf) domain: (-inf, inf)

what is the domain and range of the function f(x) = 2(5)^x + 3?

range: (3, inf) domain: (-inf, inf)

which option shows the correct steps to find the inverse of f(x) = 5sqrt(7-x) + 3?

step 7: 7 - (x - 3)^5

nick started a landscaping company. the function that represents the number of clients nick has is c(t) = 3(2)^t, where c is the number of clients, and t represents time in months. which statement is true?

the horizontal asymptote is y = 0, but it does not mean anything in this situation because nick starts his company with 3 clients

certain bacteria can grow in extreme temperatures, including temperatures below 0 celsius. the relationship between the temperature and the rate of bacteria growth is shown in the graph. the x-values show the degrees, in celsius, and the y-values show growth rate in multiples per hour. which statements are true? select all that apply.

the horizontal asymptote of the function is y = 2 the growth rate of the bacteria will always be greater than 2 multiples per hour

examine the graph. increasing exponential graph with points (0, 0), (1, 2), (2, 8) select all true statements about the function.

the initial value is 0 domain: (-inf, inf) range: (-1, inf) as x approaches -inf, f(x) approaches -1, and as x approaches inf, f(x) approaches inf.

which of the following statements are true about the function f(x) = 3(0.95)^x - 5? select all that apply.

the range is (-5, inf) the function is decreasing the horizontal asymptote is -5

lesson 2

transformations of exponential functions

which graph is the correct representation of the function f(x) = 2 * 3^x + 4?

use mathway.com for the graph but it's an increasing exponential passing (0, 6)

which graph is the correct representation of the function f(x) = 4 * 3^x - 2?

use mathway.com for the graph but it's an increasing graph with point (0, 2)

which graph is the correct representation of the function f(x) = 2 * 0.5^x - 5?

use mathway.com for the graph (write only the function) but it's a decreasing exponential graph will point (0, -3)

which equation is equivalent to 3x − 5 = 4?

x = log_3 9

what is the exponential form of log_x 109 = 12?

x^12 = 109

examine the graph. increasing exponential graph with points (0, 0) and (-2, 15) what is the horizontal asymptote of the function?

y = -1

the general form of an exponential equation is y = ab^x + k. what is the general form of the following equation? y - 4 = 3^2x/7

y = 1/7 * 9^x + 4

what is the horizontal asymptote of the function?

y = 3

what is the exponential form of x = log_4 y/5?

y = 5 * 4^x

what is the exponential form of x = log_7 y-4?

y = 7^x + 4

the general form of an exponential equation is y = ab^x + k. what is the general form of the following equation? y + 1 = (3^x+1)^2

y = 9(9^x) - 1