Abeka, 2022-2023, Algebra II, Test 7

Which of the types of functions is a transcendental function?

a. rational

b. logarithmic

c. radical

d. rational

logarithmic (worth 2)

Which functions is not a one-to-one function?

a. f(x) = x²

b. f(x) = x³

c. f(x) = x - 4

d. f(x) = x

f(x) = x² (worth 2)

What is the value for the function f(x) = 3∧x⁻¹ if x = 4?

27 (worth 2)

What is the value for the function f(x) = 2e∧x if x = 4 (rounded to the hundredths place)?

109.20 (worth 2)

Which of the following transformations is represented by 2 in the following equation: f(x) = 3∧x⁻² + 5?

a. vertical reflection

b. horizontal translation

c. vertical translation

d. vertical stretch

horizontal translaion (worth 2)

Which of the following logarithmic properties is used in the following expansion: logx³ + 3logx?

a. product

b. quotient

c. inverse

d. power

power (worth 2)

(short answer) What is the argument in the logarithmic function

f(x) = log₂4?

4 (worth 3)

(short answer) To which line are inverse functions symmetric?

y = x (worth 3)

(short answer) Rewrite log₆7,776 = 5 as an exponential equation.

6⁵ = 7,776 (worth 3)

(short answer) What type of function is the inverse of a logarithmic function?

exponential (function) (worth 3)

(Using the logarithmic properties, rewrite the expressions as indicated.)

Expand the expression log xy/z.

logx + logy - logz (worth 4)

(Using the logarithmic properties, rewrite the expressions as indicated.)

Expand the expression ln x²y³.

2 lnx + 3lny (worth 4)

(Using the logarithmic properties, rewrite the expressions as indicated.)

Condense the following expression to a single logarithm:

3logx - 4logy.

log x³/y⁴ (worth 4)

(Using the logarithmic properties, rewrite the expressions as indicated.)

Condense the following expression to a single logarithm:

1/2 lnx + lny

lny√x (worth 4)

(Evaluate the logarithm using the change of base formula. Round to three decimal places.)

log₅11

1.490 (worth 4)

(Evaluate the logarithm using the change of base formula. Round to three decimal places.)

log₄200

3.822 (worth 4)

(Find the inverse function for the function listed.) f(x) = x³ + 9

f⁻¹(x) = ³√x-9 (worth 6)

(Find the inverse function for the function listed.) f(x) = 2x + 5/x

f⁻¹(x) = 5/x - 2 (worth 6)

(Solve the problem without a calculator.) 8∧x∧²∧+⁴ = 8¹³

x = ±3 (worth 7)

(Solve the problem without a calculator.) x = log₈4 + log₈16

x = 2 (worth 7)

(Solve the problem without a calculator.) log x = log (x-3) = 1

x = 5 (worth 7)

(Solve with a calculator. Round to three decimal places.)

ln (x - 4) = 7

x ≈ 1,100.633 (worth 7)

(Solve with a calculator. Round to three decimal places.)

x - log₃72 - log₃9

x ≈ 1.893 (worth 7)

(word problem. Round to two decimal places. Show your work.)

Find the final amount when $10,000 is invested for 3 years at 3%. the interest is compounded continuously using the formula A = Pe∧rt

$10,941.74 (worth 5)