Questions: Graphing Transformations of Absolute Value Functions The graph f(x)=x is shown below. Let g(x) be a transformation of f(x) shifted up 2 and right 3. Draw the graph of g(x) and write its formula below. Draw: Write the transformation of f(x)=x below. Be sure to use proper function notation.

Graphing Transformations of Absolute Value Functions The graph f(x)=x is shown below. Let g(x) be a transformation of f(x) shifted up 2 and right 3. Draw the graph of g(x) and write its formula below. Draw: Write the transformation of f(x)=x below. Be sure to use proper function notation.
Transcript text: Graphing Transformations of Absolute Value Functions The graph $f(x)=|x|$ is shown below. Let $g(x)$ be a transformation of $f(x)$ shifted up 2 and right 3. Draw the graph of $g(x)$ and write its formula below. Draw: Write the transformation of $f(x)=|x|$ below. Be sure to use proper function notation.
failed

Solution

failed
failed

Solution Steps

Step 1: Identify the Original Function

The original function given is \( f(x) = |x| \).

Step 2: Determine the Transformations

The problem states that the transformation involves shifting the graph up by 2 units and to the right by 3 units.

Step 3: Apply the Horizontal Shift

Shifting the graph to the right by 3 units means replacing \( x \) with \( x - 3 \). Thus, the function becomes \( f(x) = |x - 3| \).

Step 4: Apply the Vertical Shift

Shifting the graph up by 2 units means adding 2 to the function. Thus, the function becomes \( g(x) = |x - 3| + 2 \).

Final Answer

The transformed function is \( g(x) = |x - 3| + 2 \).

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Irene likes to study and collect maps as a hobby. Pierre prefers an easy commute so he can return home quickly. Mary enjoys playing and spending time with children. Arjun has learned classical dance. Elena is good at speaking to a large audience.
failedAnswered
f(x)=(x+9)/(x^2-81) B. There is no x-intercept. Select the correct choice below and fill in any answer boxes within your choice. A. The y-intercept is (0,-1/9). (Type an ordered pair, using integers or fractions.) B. There is no y-intercept. Find the vertical asymptote(s). Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
failedAnswered
Graph the system of inequalities. y > x^2 - 7 y <= x - 2
failedAnswered
Detective Johnson, without a search warrant, searches Tom's property while he is away and finds stolen goods linking him to burglaries. Which statement is correct regarding the admissibility of this evidence? Since the exclusionary rule only applies to confessions obtained without Miranda warnings, the evidence can be used. Under the exclusionary rule, the evidence obtained without a warrant cannot be used against Tom. Depending on how credible the evidence is, a judge will decide whether it is admissible. Because the evidence is credible, the prosecution can use the evidence against Tom.
failedAnswered
Budgeting Decision Point Managers - Google Chrome pe-xl-prod.knowdl.com/content/qualsims/accounting/budgetingsim/v2/player/#/265d911b8dd98f8f2e9d60cac9346771qualsimsaccountingbudgetingsimmillernoblesmattison7/ Decision Point: Managers Timing for your budgeting process review, including a draft of comprehensive first quarter budgets, should not be a constraint since you are only at the halfway point in the current fiscal year when you kick off your review. That being said, you can't get very far until the team determines who should be involved in the budgeting process. Which managers should participate in the budgeting process? Select an option from the choices below and click Submit. Top-level managers only since they establish the company's goals and formulate business strategies. This top-down approach for establishing the budget will ensure company resources are in line with the long-term strategic plans. Include all levels of management since managers will be more motivated by the budgets if they have a say in creating them.