Questions: Graph the function f(x)=x+8. Use the graphing tool to graph the function.

Graph the function f(x)=x+8. Use the graphing tool to graph the function.
Transcript text: Graph the function $f(x)=|x+8|$. Use the graphing tool to graph the function.
failed

Solution

failed
failed

Solution Steps

Step 1: Identify the parent function

The parent function is $f(x) = |x|$. This is the absolute value function. The graph of this function is a V shape with the vertex at the origin (0,0).

Step 2: Determine the transformation

The given function is $f(x) = |x + 8|$. The "+ 8" inside the absolute value function represents a horizontal shift. Adding a positive number inside the absolute value shifts the graph to the _left_. Therefore, the graph of $f(x) = |x + 8|$ is the graph of $f(x) = |x|$ shifted 8 units to the left.

Step 3: Locate the vertex

The vertex of the parent function $f(x) = |x|$ is at (0,0). Since the graph is shifted 8 units to the left, the vertex of $f(x) = |x + 8|$ is at (-8,0).

Final Answer:

The graph of $f(x) = |x + 8|$ is a V-shaped graph with the vertex at (-8, 0). It is the graph of the absolute value function shifted 8 units to the left.

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
What fraction of all the cards are Red or Face cards? What fraction of all the cards are neither Red nor Face cards?
failedAnswered
Find the distance between the points whose coordinates are given. [ (-4,-20),(-6,6) ]
failedAnswered
The following data represent the flight time (in minutes) of a random sample of six flights from Las Vegas, Nevada, to Newark, New Jersey, on United Airlines. 282, 260, 266, 257, 260, 267 Compute the range and sample standard deviation of flight time. The range of flight time is 25 minutes. The sample standard deviation of flight time is minutes. (Type an integer or decimal rounded to one decimal place as needed.)
failedAnswered
The accompanying data set lists the numbers of children of world leaders. Use the data to construct a frequency distribution using six classes and to create a frequency polygon. Describe any patterns.
failedAnswered
Fixed expenses are 30,000 per month and the company is selling 2,000 units per month. Required: 1-a. How much will net operating income increase (decrease) per month if the monthly advertising budget increases by 5,000, the monthly sales volume increases by 100 units, and the total monthly sales increase by 9,000? 1-b. Should the advertising budget be increased?