Fill in the blanks.

Two functions $f$ and $g$ can be combined by the arithmetic operations of $\underline{\hspace{1.5cm}},$ $\underline{\hspace{1.5cm}},$ $\underline{\hspace{1.5cm}},$ and $\underline{\hspace{1.5cm}},$ to create new functions.

In this exercise, function g is related to one of the parent functions described in the previous section. Identify the parent function f.

$$g(x)=\dfrac{1}{2} \sqrt{x}$$

In this exercise, function g is related to one of the parent functions described in the previous section. Use function notation to write g in terms of f.

$$g(x)=-2 x^2+1$$

The balance in the unearned fees account, before adjustment at the end of the year, is $272,500. Journalize the adjusting entry (include an explanation) required if the amount of unearned fees at the end of the year is$189,750.

On July 1, the cash account balance was $37,450. During July, cash payments totaled$115,860 and the July 31 balance was $29,600. Determine the cash receipts during July.

On July 1 , the cash account balance was $37,450. During July, cash payments totaled$115,860 and the July 31 balance was $29,600. Determine the cash receipts during July.

On July 1, the cash account balance was $37,450. During July, cash payments totaled$115,860 and the July 31 balance was $29,600. Determine the cash receipts during July.

For the numbers $2$ through $9$ on a telephone keypad (see figure), create two relations: one mapping numbers onto letters, and the other mapping letters onto numbers. Are both relations functions? Explain.

Fill in the blanks.

If the composite functions $f(g(x))$ and $g(f(x))$ both equal $x$, then the function $g$ is the $\underline{\hspace{1.5cm}}$ function of $f$.

Emerson Company is a small editorial services company owned and operated by Suzanne Emerson. On October 31, 20Y6, Emerson Company’s accounting clerk prepared the following unadjusted trial balance:

The data needed to determine year-end adjustments are as follows:

a. Unexpired insurance at October 31, $550.
b. Supplies on hand at October 31,$610.
c. Depreciation of building for the year, $10,920.
d. Depreciation of equipment for the year,$7,830.
e. Unearned rent at October 31, $2,050.
f. Accrued salaries and wages at October 31,$2,550.
g. Fees earned but unbilled on October 31, $9,140.

Required:

1. Journalize the adjusting entries using the following additional accounts: Salaries and Wages Payable, Rent Revenue, Insurance Expense, Depreciation Expense—Building, Depreciation Expense—Equipment and Supplies Expense. Refer to the chart of accounts for the exact wording of the account titles. CNOW journals do not use lines for journal explanations. Every line on a journal page is used for debit or credit entries. CNOW journals will automatically indent a credit entry when a credit amount is entered.
2. Determine the balances of the accounts affected by the adjusting entries and prepare an adjusted trial balance.

Fill in the blanks.

A relation that assigns to each element $x$ from a set of inputs, or $\underline{\hspace{1.5cm}}$ , exactly one element $y$ in a set of outputs, or $\underline{\hspace{1.5cm}}$, is called a $\underline{\hspace{1.5cm}}$.

Fill in the blanks.

The graph of a function $f$ is the collection of $\underline{\hspace{1.5cm}}$ $(x, f(x))$ such that $x$ is in the domain of $f$.

Determine whether the equation represents $y$ as a function of $x$.

$$16 x-y^4=0$$

Use a graphing utility to graph the function and approximate (to two decimal places) any relative minimum or relative maximum values.

$$h(x)=(x-1) \sqrt{x}$$