Exponential Graphs
Transformations of Exponential Functions
Logarithms
Talk the Talk
Mix
100
Does this function represent exponential GROWTH or DECAY?
f(x) = 1.2(0.99)x
DECAY
100
Consider the function:
f(x)=2(x-1) +5.
What is the parent function?
f(x) = 2x
100
What is the OUTPUT of a LOGARITHMIC function? Use one word!
an EXPONENT
100
What do you call of 2 value in the exponential equation?
f(x)=2∙5^x
INITIAL VALUE; starting point
100
Evaluate:
log7 721
21
200
Write the END BEHAVIOR of this graph.
x → -∞, y →
x → +∞, y →
x -> -oo, y -> 3
x -> +oo, y -> +oo
200
Consider the function: f(x) = 3(x+2) - 8.
Describe all transformations the function has undergone from the parent function.
2 units left
8 units down
200
Evaluate the logarithms below:
a) log2(64)
b) log5(125)
a) 6
b) 3
200
What do you call of 5 value in the logarithmic equation?
y = log5 x
Base
200
Double Jeopardy!!
How many times b more than a if
log a = 2 and log b = 4?
100
If log a = 2, then a=100
If log b = 4, then b=10000
b/a=10000/100=100
300
Does this exponential function model GROWTH or DECAY?
y=0.75(7/6)^x+3
GROWTH
300
Identify the TRANSFORMATIONS applied to f(x) in order to create g(x). Be specific.
f(x) = 4x
g(x) = -2(4)x-3 - 5
3 units right; down 5 units
REFLECTED over the x-axis
VERTICAL STRETCH by a factor of 2
300
Write the logarithm in EXPONENTIAL form.
7^-2=1/49
300
What can you say about the graphs of exponential and logarithmic functions? (How do they compare to each other?)
their graphs are symmetrical (reflected) along the line y=x.
300
Solve for x:
log3 x = -4
x = 1/81
Solution:
3-4 = (1/3)4 = 1/81
400
Write the exponential equation for the table below.
f(x) = 5(3)x
400
The blue graph is of f(x)=2x. Find the equation of the green graph g(x) which has been transformed.
g(x)=2^((x-4))-3
400
Estimate the value of log3 (90)
xapprox4.1
400
Convert to exponential form: log3 81 = 4
34 = 81
400
Solve for x:
log4 (-16) = x
undefined
The domain of the logarithmic function is any positive number.
500
Write the equation of the exponential graph.
y=0.5(1.5)^x
500
Where is the asymptote for this function? Is it vertical or horizontal?
f(x)=2(x-3) + 2.
horizontal asymptote at 2
500
Evaluate: log 2 + log x = 4
x=5000
500
Convert this to logarithmic form: 45=1024
log4 1024 = 5
500
Solve for x: log6x = 5
x = 7776