Domain and Range
What is the domain of the function f(x)=∣x−3∣
(-infinity, infinity)
What is the vertex of the function f(x)=∣x+2∣−3
(-2, -3)
What transformation occurs to the graph of f(x)=∣x∣ to get g(x)=∣x∣+4?
The graph is shifted up 4 units.
Solve the equation ∣x−4∣=3 and state the number of solutions.
2 solutions x=(1, 7)
Is the following a Conjunction or Disjunctions? ∣x−5∣<2
Given the function g(x)=∣2x+1∣, what is its range?
[0, infinity)
Describe the axis of symmetry for the absolute value function g(x)=∣x−1∣
The axis of symmetry is x=1
If the function h(x)=∣x−3∣ is transformed to k(x)=−∣x−3∣, what happens to the graph?
It is a reflection across the x axis
Solve the equation ∣2x+4∣=10.
2 solutions x - (-7, 3)
What does the solution set look like for the inequality ∣x+3∣≥4 in interval notation?
(-infinity, -7] or [1, infinity)
How would you express the domain of h(x)=∣x2−4∣ using interval notation?
(-infinity, infinity)
How does the vertex of h(x)=∣3x−6∣+2 relate to its transformations?
The vertex is (2, -2). The graph has been shifted 2 units to the right and 2 units up.
Describe the transformation of the graph of m(x)=∣x∣ to n(x)=∣2x∣+1.
This is a Horizontal Compression and shift up 1 unit
Solve the equation ∣3x−5∣+2=11
2 solutions x= ( -4/3, 14/3)
How would you express the solution of the inequality ∣2x−1∣<3 in set notation?
-1<x<2
For the function k(x)=∣x∣+3, identify its domain and express it in set notation.
Domain: (-infinity, infinity) Range: [3, infinity)
What is the vertex of the function k(x)=−∣x+4∣+1, and how does it relate to the range of the function?
The vertex is (-4, 1). It is the highest point on the graph, therefore the range is (-infinity, 1]
How does multiplying the function p(x)=∣x∣ by -1 affect the y values of the function and ultimately the graph?
It makes all of the y values negative thereby reflecting the graph across the x- axis.
If the equation ∣x∣=−5 is presented, what can you conclude about its solutions?
There would be no solutions because absolute value cannot equal a negative.
Given the inequality ∣x+2∣>5 solve for x and give an example of a value that is a solution to the inequatlity.
(−∞,−7)∪(3,∞) Any number between -7 and 3 but not equal to -7 or 3
Explain how to determine the range of the absolute value function m(x)=−∣x−2∣+5
The vertex is (2, 5) and the graph is reflected. So that means 5 is the highest y value on the graph. Therefore the range is (-infinity, 5]
Determine the axis of symmetry for the function m(x)=∣2x+5∣.
The axis of symmetry is x=-5/2
Explain how the graph of q(x)=∣x+1∣−2 is transformed from the parent function f(x)=∣x∣ and what is the domain and range of the transformed function?
Shifted 1 left and 2 down. Domain is all real numbers, Range is [-2, infinity)
Given the equation 1/2∣x−2∣+5=12, explain the steps to solve for x.
Start by isolating the absolute value. Subtract 5 from both sides of the equation. The divide both sides (or multiply by 2) This will result with ∣x−2∣=14. Then split into two equations x-2=14 and x-2=-14. Add 2 to both sides of each equation. You'll get x =16 and -12. Finally, check each solution by subbing into the original equation. Both solutions work.
Solve the inequality ∣3x−4∣≤2, and explain how the solutions would be represented on a number line?
[2/3, 2]You would plot solid points at 2/3 and 2 and shade in between the values.