Pre Calculus 1st Semester Final Review

Find the amount in a savings account at the end of 5 years if the amount originally deposited is $6000 and the interest rate is 7% compounded quarterly.

$8488.67

Find the domain of the function. NO CALC f(x)=log(7-x)

(-∞,7)

Give the coordinates of the hole in the graph of the following equation. NO CALC f(x)= (x²-16) / (x²+x-20)

(4,8/9)

Convert the angle in radians to degrees. NO CALC -π

-180°

Which angle is not a coterminal angle to 140°? NO CALC

-40°

Solve the problem. NO CALC Suppose that f(x)=2^x. If f(x)=1/64, what is x?

-6

Convert the angle in degrees to radians. NO CALC -90⁰

-π/2

Find the exact value of the expression. NO CALC sin^-1(0)

0

Find the exact value. NO CALC tan0

0

Find the exact value. NO CALC tanπ

0

The function D(h)=8e^(-0.4h) can be used to determine the milligrams D of a certain drug in a patient's bloodstream h hours after the drug has been given. How man milligrams will be present after 6 hours?

0.73 mg

What is the domain of the function f(x)=√x³-6x² ?

0∪[6,∞)

Use the properties of logarithms to find the exact value of the expression. NO CALC log₄24-log₄6

1

Solve the equation. 3^(6x-1)=(e^4)^-x

1/10

Use the fact that trigonometric functions are periodic to find the exact value of the expression. cos420°

1/2

Find the exact value of the logarithmic expression. NO CALC log₁₀100

2

Change the logarithmic expression to an equivalent expression involving an exponent. NO CALC log₃1/27=-3

3^-3=1/27

A radio transmission tower is 150 feet tall. How long should a guy's wire be if it is to be attached 5 feet from the top and is to make an angle of 20° with the ground? Give your answer to the nearest tenth of a foot.

424.0 ft

A straight tail with a uniform inclination of 11⁰ leads from a lodge at an elevation of 600 feet to a mountain lake at an elevation of 9000 feet. What is the length of the trail (to the nearest foot)?

44,023 ft

Find the measure of the reference angle of an angle with a measure of 310°. NO CALC

50°

Solve the triangle. B=20°, C=30°, a=2

A=130°, b=0.89, c=1.31

Solve the triangle. A=60°, B=100°, a=1

C=20°, B=100°, a=1

Name the quadrant in which the angle θ lies. NO CALC sec θ < 0, tan θ < 0

II

Name the quadrant in which the angle θ lies. NO CALC cos θ <0, csc θ <0

III

Suppose that ln2=a and ln5=b. Use properties of logarithms to write each logarithm in terms of a and b. NO CALC ln5/2

b-a

Determine whether the relation represents a function. If it is a function, state the domain and range. NO CALC 3→9 5→15 7→21 9→27

function domain: {3,5,7,9} range: {9,15,21,27}

Change the exponential expression to an equivalent expression involving a logarithm. NO CALC 7²=49

log₇49=2

Which of the following choices is equivalent to log8/log7? NO CALC

log₇8

Give the equation of the oblique asymptote, if any, of the function. H(x) = (4x²-4x-6) / (5x²-8x+3)

none

Find the exact value. NO CALC cot0

undefined

Find the vertical asymptotes of the rational function. NO CALC R(x)=(x+8)/(x²-36)

x=-6, x=6

Find the function that is finally graphed after the following transformations are applied to the graph of y=|x|. The graph is shifted right 3 units, stretched by a factor of 3, shifted vertically down 2 units, and finally reflected across the x-axis. NO CALC

y=-(3|x-3|-2)

Give the equation of the horizontal asymptote, if any, of the function. NO CALC H(x)= (7x-2) / (x-8)

y=7

Give the equation of the slant asymptote, if any, of the function. T(x)= (x²-7x+3) / (x+9)

y=x-16

Write an equation that results in the indicated translation. NO CALC The squaring function, shifted 7 units downward

y=x²-7

Find the real solutions of the equation. x⁴-8x³+16x²+8x-17=0

{-1,1}

Find the real solutions of the equation. 2x⁴-2x³+x²-5x-10=0

{-1,2}

Solve the equation. 3^(1+2x)=27

{1}

Solve the equation. 2+8lnx=11

{3^(9/8)}

Convert the angle in degrees to radians. 36⁰

π/5

Find the exact value of the expression. NO CALC cos^-1 ((√3)/2)

π/6