algebra 2b - exam 1

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

https://assets.learnosity.com/organisations/625/a1570a35-80c9-40a1-8160-8e73169888c6.png

sketch the graph of the exponential function f(x) = 3^x - 3. which graph is the correct representation of the function?

https://assets.learnosity.com/organisations/625/d6c6f4bb-421d-4e15-aa34-f28e5281d163.png

which graph shows f(x) = 4^x - 4 and the dilation g(x) = 1/4(4^x - 4)?

https://assets.learnosity.com/organisations/625/e20c0651-5bd4-4ecb-8873-2a1eb7aa2755.png

which equation is equivalent to 3^r + 16 = q?

r = log_3 (q - 16)

examine the graph. https://assets.learnosity.com/organisations/625/c650aec0-9e9d-4f17-8408-5a6a91f474bf.png select all true statements about the function.

the initial value is 1. domain: (−∞, ∞) range: (−1, ∞) as x approaches −∞, f(x) approaches ∞, and as x approaches ∞, f(x) approaches −1.

what is the closest approximate value of log 0.2?

-0.7

what is the closest approximate value of log_6 95?

2.5

what is the exponential form of log_2 32 = 5?

2^5 = 32

what is the value of log 1,000?

3

what is the value of log_5 125?

3

what is the closest approximate value of ln(29)?

3.4

a rare baseball card that was purchased increases in value over time. the function c(t) is represented on the following graph, where c represents the value of the card, and t is time in years since the card was purchased. what is the initial value, and what does it represent?

XXX the initial value is 0 and it represents the lowest value of the card.

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

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

a function is translated from f(x) = 9 * 3^x - 2 to g(x) = 9 * 3^x+4 - 2. what is the effect on f(x)?

f(x) moves 4 units to the left

the function f(x) = 3 * 4^x + 5 is translated to become g(x) = 3 * 4^x - 2. what is the effect on f(x)?

f(x) moves 7 units downward

which option shows the correct steps to find the inverse of f(x) = 3√4-x - 2?

f^-1(x) = 4 - (x + 2)^3

given f(x) = 11^x, what is f^-1(x)?

f^-1(x) = log_11 x

the graph shows a dilation of the preimage f(x) = 2^x + 3 to become g(x). what is the transformation rule and what is the function rule of g(x)?

g(x) = -2f(x) g(x) = -2 * 2^x - 6

the general form of an exponential equation is y = ab^x + k. what is the general form of the following equation? y - 3 = 4(5^2x+1)

y = 20(25^x) + 3