WRITE THE EQUATION FROM THE GRAPH OF ABSOLUTE VALUE FUNCTION
Subscribe to our ▶️ YouTube channel 🔴 for the latest videos, updates, and tips.
Problem 1 :
Write the equation of the graph. Then give its range as an inequality.
Problem 2 :
Problem 3 :
Problem 4 :
Problem 5 :
Problem 6 :
Problem 7 :
Describe and correct the error in graphing the function.
Problem 8 :
Describe and correct the error in graphing the function.
Answer Key
1) y = 1 |x +1| + 2
Range is 2 ≤ y ≤ ∞
2) y = -1 |x + 3| - 2
Range is -2 ≤ y ≤ -∞
3) y = -2 |x - 2| + 3
Range is 3 ≤ y ≤ -∞
4) y = (1/2) |x + 2| - 3
Range is -3 ≤ y ≤ ∞
5) y = (-3/4) |x - 1|
Range is 1 ≤ y ≤ -∞
6) y = (2/3) |x + 2|
Range is -2 ≤ y ≤ ∞
7) By observing the graph, the function opens up but the vertex is at (-1, -3) and that is the error.
8) By observing the graph, it opens up. But it should be open down and that is the error.
Graph the following absolute value function :
by finding the following.
(i) Vertex
(ii) Slope
(iii) Direction of opening
(iv) x and y intercepts
(v) Domain and range
(vi) Increasing and decreasing
Problem 1 :
y = 3|x - 3|
Problem 2 :
Graph
f(x) = |x − 4| − 1
Determine when the function is positive, negative, increasing, or decreasing. Then describe the end behavior of the function.
Problem 3 :
A function g is increasing when x < 2, decreasing when x > 2, and has a range of (−∞, −2). Use the given values to complete the function. Do not use any value more than once.
-2 0 2 - 1
Problem 4 :
Graph each absolute value function f with the given characteristics.
a) f has a range of (−∞, 1), and a graph that is symmetric about the line x = −2 and has a y-intercept of −5.
b) f is positive over the intervals (−∞, 0) and (4, ∞), negative over the interval (0, 4), and the minimum value is −4.
Answer Key
1)
Vertex is at (3, 0).
x-intercept is (3, 0).
y-intercept is at (0, 9).
The curve will open up.
Domain and range :
- All real values is domain.
- Range is 3 ≤ y ≤ ∞
Increasing and Decreasing :
- To the left of minimum, it is decreasing.
- To the right of minimum, it is increasing.
2)
- Vertex is at (4, -1)
- Opening up.
- x-intercepts are (5, 0) and (3, 0)
- y-intercept is (0, 3)
- Positive when x < 3 and x > 5
- Negative when 3 < x < 5
Increasing or decreasing :
Decreasing on (-∞, 4)
Decreasing on (4, ∞)
End behavior :
When x -> -∞ y --> ∞
When x -> ∞ y --> ∞
3) y = |x - 2|
4)
Because the graph is symmetric about x = −2, the x-value of the vertex is −2. Because the range is (−∞, 1), the y-value of the vertex is 1.
Plot the vertex (−2, 1). Because the y-intercept is − 5, plot the point (0, − 5) and its reflection in the line of symmetry, (−4, −5). Then draw the graph.
Problem 1 :
f(x) = -3│x - 4│ + 3
Problem 2 :
f(x) = -1/2│x - 2│ + 4
Problem 3 :
f(x) = │x - 3│ - 2
Subscribe to our ▶️ YouTube channel 🔴 for the latest videos, updates, and tips.
Recent Articles
-
Finding Range of Values Inequality Problems
May 21, 24 08:51 PM
Finding Range of Values Inequality Problems -
Solving Two Step Inequality Word Problems
May 21, 24 08:51 AM
Solving Two Step Inequality Word Problems -
Exponential Function Context and Data Modeling
May 20, 24 10:45 PM
Exponential Function Context and Data Modeling