Questions: Graph the equation shown below by transforming the given graph of the parent function. y=4 sqrt(x-1)

Graph the equation shown below by transforming the given graph of the parent function. y=4 sqrt(x-1)
Transcript text: Graph the equation shown below by transforming the given graph of the parent function. \[ y=4 \sqrt{x-1} \]
failed

Solution

failed
failed

Solution Steps

Step 1: Identify the Parent Function

The parent function for the given equation \( y = 4\sqrt{x} - 1 \) is \( y = \sqrt{x} \).

Step 2: Apply Vertical Stretch

The coefficient 4 in \( y = 4\sqrt{x} - 1 \) indicates a vertical stretch by a factor of 4. This means that each y-coordinate of the parent function \( y = \sqrt{x} \) is multiplied by 4.

Step 3: Apply Vertical Shift

The term \(-1\) in \( y = 4\sqrt{x} - 1 \) indicates a vertical shift downward by 1 unit. This means that each y-coordinate of the vertically stretched function is decreased by 1.

Final Answer

The graph of the equation \( y = 4\sqrt{x} - 1 \) is obtained by vertically stretching the parent function \( y = \sqrt{x} \) by a factor of 4 and then shifting it downward by 1 unit. The resulting graph is shown in the image provided.

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Solve the equation for all real solutions in simplest form. 3 p^2 - 3 p - 6 = -2
failedAnswered
The adjusted trial balance of Estella Real Estate Appraisal at June 30, 2024, follows: Close expenses for the period. Date Accounts and Explanation Debit Credit Jun. 30 Income Summary Clos. (2) Insurance Expense 4,800 Salaries Expense 30,000 Supplies Expense 400 Interest Expense 8,000 Utilities Expense 2,900 Depreciation Expense-Building 7,900 To close expenses. Data table Account Title Debit Credit Cash 4,300 Accounts Receivable 4,500 Office Supplies 2,400 Prepaid Insurance 2,500 Land 13,500 Building 79,000 Accumulated Depreciation- Building 26,000 Accounts Payable 19,300 Interest Payable 8,000 Salaries Payable 1,900 Unearned Revenue 5,700 Notes Payable (long-term) 37,000 Common Stock 7,000 Retained Earnings 34,000 Dividends 27,100 Service Revenue 48,400 Insurance Expense 4,800 Salaries Expense 30,000 Supplies Expense 400 Interest Expense 8,000 Utilities Expense 2,900 Depreciation Expense-Building 7,900 Total 187,300 187,300
failedAnswered
Question 5 of 10 A digital scale reports a 10 kg weight as weighing 8.975 kg . Which of the following is true? A. The scale is both accurate and precise. B. The scale is precise but not accurate. C. The scale is neither precise nor accurate. D. The scale is accurate but not precise.
failedAnswered
For the function f(x) = 4x^2 + 6x - 1, evaluate f(a + h).
failedAnswered
Consider two pieces of tubing 1/2 in and 3/4 in, two washers 3/16 in each, and a nut 1/16 in thick. The smallest length of a bolt that will pass through all these is in. (Type a whole number, proper fraction, or mixed number.)