Characteristics of Functions
The range of an absolute value parent function
[0, positive infinity]
In the transformation equation y=af(b(x-c))+d, what transformation is created by the d value?
Vertical Shift
The leading term in the function
f(x) = 4x2 + 7x - 5x3 + 10 is
-5x3
How do you find the vertical asymptotes of a rational function?
Set the denominator equal to 0
log x has a base of ____
10
The quadratic parent function is an example of what type of symmetry?
Even
Compared to the parent function y = x2, what transformation is applied to create y= x2 + 3
Shift up 3 units
For f(x) = -3x4 - 6x2 + 15, complete the end behavior statement:
As x approaches positive infinity, f(x) approaches___
negative infinity
The end behavior (horizontal asymptote) for f(x) = (2x - 1)/(x2 + 1) is _____
y = 0
ln x = 4 written as an exponential equation is ___
e4 = x
For the exponential growth parent function, as
x approaches negative infinity, what does f(x) approach?
0
What is the equation for the vertical asymptote for the function f(x) = 2 + log (x + 1)
x = -1
Find the remainder when (x3 -3x2 + 4x + 5) is divided by (x - 2)
9
The domain for f(x) = (x + 1)/[(x+1)(x-1)] is
(-infinity, -1) U (-1, 1) U (1, infinity)
Express as a log equation: 3(4x)=15
log 4 5 = x
What is the equation for the rational parent function?
y = 1/x
If f(x) = x + 1 and g(x) = 3x2 - 1, what is
(f o g )(x)?
(f o g)(x) = 3x2
Find the remainder when
(2x2 - 1) is divided by (x + 3)
17
The roots of f(x) = (x2 + 5x + 6)/(x2 - 4) is/are
x = -3
f(t) = 10(2)t represents the number of bacteria in a dish after t hours. How many bacteria were in the dish initially?
10
The domain of the logarithmic parent function is...
(0, positive infinity)
Find the inverse equation for f(x) = 3x + 2.
f-1(x) = (x-2)/3
f(x) = 4x5 - 2x3 - x2 + 2x + 10 has a maximum of _______ real solutions and a maximum of ______ turns
5 real solutions
4 turns
The y-intercept for f(x)=(x + 1)/(x2 + 2x) is ____
undefined/does not exist
Condense into a single log:
3log x - log y - log a
log [(x3)/(ya)]