Chapter 3- Precalc and Trig

Pataasin ang iyong marka sa homework at exams ngayon gamit ang Quizwiz!

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


Kaugnay na mga set ng pag-aaral

Endocrine System - Hormones & Glands

View Set

Chapter 67 Care of the Normal Newborn 4

View Set

Q UNIT 5 Last one before exam Federal bureaucracy cabinet, executie departments independent agencies

View Set

Hadoop, Linux, and Big Data - Week 3 Revature

View Set

FMcases 5 - Palpitations (thyroid)

View Set