Algebra 2 Unit 11 Part A Review Sheet Name: ________

1) What point does the graph of 𝑓(𝑥) = 𝑙𝑜𝑔1

5

(𝑥) pass through?

(1) (5, 1)

(2) (1

5, 1)

(3) (1

5, −1)

(4) (5, −1)

2) Which statement about the graph of the equation is not true?

1) It is asymptotic to the x-axis. 2) The domain is the set of all real numbers. 3) It lies in Quadrants I and II. 4) It passes through the point .

3) If and , for which value of x is ?

1) and 2) and 4 3) and 0 4) 4 and 0

4) If 𝑓(𝑥) = 3(5)𝑥, determine the coordinates of the y-intercept of the function defined by

𝑓(𝑥) + 4. (1) (0, 9) (3) (0, 7) (2) (7, 0) (4) (0, 5) 5)

6)

7) Which statement about the graph of 𝑓(𝑥) = 𝑙𝑜𝑔9𝑥 is false?

(1) The domain is the set of positive reals.

(2) The equation of the asymptote is y=0.

(3) The range is all real numbers.

(4) The graph has no y-intercept.

8) Solve the following equation graphically for all values of x to the nearest hundredth:

(1

4)

𝑥−2

= 𝑙𝑜𝑔4(𝑥)

9) On the same set of axes, sketch the functions 𝑓(𝑥) = log2(𝑥) and 𝑔(𝑥) = −log2(𝑥 − 3).

Describe a transformation that takes the graph of 𝑓 to the graph of 𝑔.

10) Sketch the graph of this pair of functions on the same coordinate axes.

32)(

2)(

1

x

x

xg

xf

Describe the graph of g(x) as a series of transformations on the graph of f(x). State the equation of the asymptote for g(x).

Determine the domain and range of g(x).

Describe the end behavior of g(x).

11) Graph 𝑓(𝑥) = log4(𝑥 − 1) − 3 on the set of axes below. Use an appropriate scale to include any

intercepts.

12) Two functions are given below.

𝑓(𝑥) = log2 𝑥 𝑔(𝑥) = log2(𝑥 + 5)

Describe the graph of g(x) as a series of transformations on the graph of f(x). What is the coordinate of the x-intercept of function g?

13) The level of a drug, in milligrams, in a patient’s bloodstream is a function of time, t, in hours, according to the formula 𝑔(𝑡) = 300(0.8)𝑡. Graph 𝑔(𝑡)over the interval 0 ≤ 𝑡 ≤ 10, on the set of axes below.

Determine, to the nearest hour, when there will be 50 milligrams of the drug left in the patient’s bloodstream. Justify your response.

14) Describe and correct the error a student made in finding the inverse of the exponential function 𝑓(𝑥) = 5𝑥−6 + 2.

𝑦 = 5𝑥−6 + 2 𝑥 = 5𝑦−6 + 2 𝑥 − 2 = 5𝑦−6 𝑦 − 6 = log5 𝑥 − 2 𝑦 = log5 𝑥 − 2 + 6 𝑦 = log5 𝑥 + 4 𝑓−1(𝑥) = log5 𝑥 + 4 15) Find the inverse of each of the following functions.

a. 𝑓(𝑥) = 𝑒𝑥−5

b. 𝑔(𝑥) = 7 log(1 + 9𝑥)

16) Describe the transformation applied to the graph of 𝑝(𝑥) = 2𝑥 that form the new function

𝑞(𝑥) = 2𝑥−3 + 4.

17) Graph the following function on the axes below.

𝑓(𝑥) = 𝑙𝑜𝑔3(2 − 𝑥) State the domain of 𝑓. State the equation of the asymptote.