Honors Advanced Math II
Practice
Graphs of Exponential & Logarithmic Functions
Hi! My name is________________________________and today is_____________________________.
NO CALCULATORS
1. Write an equation for an exponential function that has a y-intercept of 7, a horizontal asymptote at
y = 1, and goes through the point (3, 49).
2. First, graph the function f (x) = log 4 x on the grid below. You should have at least 3 points
clearly marked and labeled.
a. Now, in color, graph the
function
g(x) = log 4 (4x + 8) + 1 .
6
4
You should have at least 3
points clearly marked and
labeled. (HINT: It may help
to use a property of logs to rewrite the equation first.)
2
-5
5
10
-2
-4
-6
b. Algebraically find the x- and y-intercept(s) of g(x). Show your work. (HINT: You will
get fractional answers.)
c. Re-write g(x) as logarithmic function of base 10.
Honors Advanced Math II
Practice
Graphs of Exponential & Logarithmic Functions
3. Write an equation for an exponential function that has a y-intercept of 5, a horizontal asymptote at
y = –2 , and goes through the point (–1, 19).
4. First, graph the function f (x) = log 7 x on the grid below. You should have at least 3 points
clearly marked and labeled.
a. Now, in color, graph the
function
€ ⎛ 1
⎞
g(x) = log 7 ⎜ x −1⎟ + 4 .
⎝ 7
⎠
You should have at least 3
points clearly marked and
labeled. (HINT: It may help
€
to use a property of logs to rewrite the equation first.)
6
4
2
-5
5
10
-2
-4
-6
b. Algebraically find the x- and y-intercept(s) of g(x). Show your work. (HINT: You will
get fractional answers.)
c. Re-write g(x) as logarithmic function of base B.
Honors Advanced Math II
Practice
Graphs of Exponential & Logarithmic Functions
5. First, graph the function f (x) = log 2 x on the grid below. You should have at least 3 points
clearly marked and labeled.
a. Now, in color, graph the
function
€
g(x) = 8log 2 4 4 x +12 .
You should have at least 3
points clearly marked and
labeled. (HINT: It may help
€
to use a property of logs to rewrite the equation first.)
6
4
2
-5
5
10
-2
-4
-6
b. Algebraically find the x- and y-intercept(s) of g(x). Show your work. (HINT: You will
get an answer in terms of log2 for the y-intercept and a fractional answer for the root.)
c. Re-write g(x) as logarithmic function of base E.