Chapter 3- Precalc and Trig
find the domain f(x)=log∨3∧√x+1
(-1,∞)
sketch the graph y=-4+log∨2∧(7-x) find the domain, range, and vertical asymptote
(-∞,7) (-∞,∞) x=7
find the domain f(x)=2-4log∨8∧[x/4 -3]
(12,∞)
sketch the graph y=log∨2∧(x-2) find the domain, range, and vertical asymptote
(2,∞) (-∞,∞) x=2
find the domain f(x)=log∨3∧(x-8)
(8,∞)
find the logarithm log∨2∧1/8
-3
evaluate (-4)³
-64
simplify the given exponential expression (-4x²y⁵)³
-64x⁶y¹⁵
simplify (-a³/b⁵)⁵
-a¹⁵/b²⁵
evaluate log∨15∧1
0
for the exponential function f(x)=5¹⁻x, evaluate f(3.4). use a calculator if necessary
0.021
4^log∨4∧9 + log∨3∧3∧-8
1
divide t⁸/t⁸
1
evaluate the expression (-6)⁰
1
simplify (7⁻²)²
1/2401
multiply the following: (-1/7)²
1/49
write 9⁻² as an expression using only positive exponents
1/9²
express in simplest form (r³s⁵)⁻²
1/r⁶s¹⁰
write the statement in exponential form log∨100∧1000000=3
100^3=1000000
evaluate 2^log∨2∧7 - 7∧log∨7∧5
2
The number of bacteria growing in an incubation culture increases with time according to n(t)=6,100(4)^t, where t is time in days. After how many days will the number of bacteria in the culture be 97,600?
2 days
write in exponential form log∨2∧1=0
2^0=1
evaluate log∨7∧√343
3/2
evaluate (6/7)²
36/49
convert to an exponential equation log∨3∧9=2
3^2=9
evaluate the expression 4^log∨4∧9 + log∨8∧8∧-5
4
Write an equation of the form f(x)=a^x+b from the points (0,3) and (1,5.4). Then compute f(3).
41.30
write in exponential form log∨5∧1=0
5^0=1
simplify 10^log(6)
6
evaluate 4³
64
simplify using the quotient rule, if possible. 6⁷/6³
6⁴
log∨6∧6∧8
8
for the exponential function f(x)=(1/3)¹⁻⁴x, evaluate f(3/4)
9
convert to exponential equation log∨9∧(1/729)=-3
9^-3 =1/729
evaluate log∨√4 ^81
=4
For the exponential function f(x)=ax, a>0, a≠1, the domain is ______ and the range is ______.
Domain: (-∞,∞) Range: (0,∞)
For the exponential function f(x)=a^x , a>0 , a≠1, the domain is ________ and the range is ________
Domain: (-∞,∞) Range: (0,∞)
evaluate the expression (ab)¹
ab
simplify (c⁻⁴)⁻⁹
c³⁶
multiply and simplify c¹⁷ x c⁻²
c¹⁵
change the logarithmic statement to an equivalent statement involving an exponent ln17=x
e^x=17
For the exponential function f(x)=1−3^−x, evaluate f(2).
f(2)=8/9
Find the function of the form f(x)=cax that contains the two given graph points. (1,1) and (2,4)
f(x)= 1/4 x 4^x
Write an equation of the form f(x)=ax+b from the given points: (-2,2) (-1,0). Then compute f(2).
f(x)=(1/2)^x -2 f(2)=-7/4
the function which contains the two graph points (1,1) and (2,7) is
f(x)=1/7 • 7^x
Give an equation of the form f(x)=a^x to define the exponential function whose graph contains the point (2,16)
f(x)=4^x
Find the exponential function of the form f(x)=c•ax that contains the two points shown below. (0,5) and (3,40)
f(x)=5 x 2^x
Find the exponential function of the form f(x)=c•a^x that contains the two points shown below. (0,7) and (3,56)
f(x)=7 • 2^x
State whether the following statement is true or false. The graph of log∨a∧x, a>0, a≠1 is an increasing function.
false
Given the function find h(−4). h(x)=(1/3)^1-x
h(-4)=1/243
Starting with the graph of y=ex, use transformations to sketch the graph of the function and state its horizontal asymptote. f(x)=-e^(x-5)+1
horizontal asymptote is y=1
Starting with the graph of y=ex, use transformations to sketch the graph of the function and state its horizontal asymptote. f(x)=9-e^-x
horizontal asymptote is y=9
write in logarithmic form (1/2)^-3=8
log∨1/2∧8=-3
convert to logarithmic equation 10^3=1000
log∨10∧1000 =3
convert to a logarithmic equation 10∧6=1000000
log∨10∧1000000=6
convert to a logarithmic equation 5^-3=0.008
log∨5∧0.008=-3
Write the equation in its equivalent logarithmic form. 9^2=81
log∨9∧81=2
write the given exponential equation in logarithmic form a^3 + 4=15
log∨a∧11=3
write in logarithmic form a^2 + 1=13
log∨a∧12=2
write the given exponential equation in logarithmic form 4a^4 -5=0
log∨a∧5/4 = 4
is the following an exponential function y=3^5
no
is the following an exponential function? y=x^2
no
is the following an exponential function? y=x^√x
no
divide and simplify n²/n⁻⁴
n⁶
simplify. assume all variables represent non-zero numbers (m²/n³)⁻²
n⁶/m⁴
describe the transformations from y=2^x to y=5-2^-x
reflect the graph of y=2^x across the y-axis, then across the x-axis, and then shift up 5 units
Sketch the graph of the following function. Describe how the graph can be obtained from the graph of the basic exponential function 2^x. f(x) 3 x 2^(x-2)+3
shift the graph of y=2^x right 2 units, stretch it vertically, and shift it up 3 units
Sketch the graph of the function and check the graph with a graphing calculator. Before doing so, describe how the graph of the function can be obtained from the graph of a basic exponential function. f(x)=e^-x-4
shift the graph of y=e^x right 4 units and then reflect it across the y-axis
Sketch the graph of the function and check the graph with a graphing calculator. Before doing so, describe how the graph of the function can be obtained from the graph of a basic exponential function. f(x)=2^x+5
start with the graph of y=2^x. shift the graph 5 units to the left
Simplify using the product rule, if possible. m² x n³
the expression cannot be simplified
let y=e^-x. As x→∞, y→0. state whether this statement is true or false
true
The horizontal asymptote of the graph of y=(1/3)^x is the ____
x-axis
simplify (yx⁴)(xz²)(yz)
x⁵y²z³
graph f(x)=-e^(x-4) -3 and what is the horizontal asymptote
y=-3
graph g(x)=e^x+2 whats the asymptote domain range
y=0 domain: (-∞,∞) range: (0,∞)
Write an equation of the graph in its final position. The graph of y=5^x is translated 6 units to the left and then 9 units upward.
y=5^(x+6) +9
is the following an exponential function y=4^x
yes
is the following an exponential function: y=3^x
yes
