AA2-9 graphing absolute value functions A-level

Last updated over 4 years ago

10 questions

AA2-9 graphing absolute value functions A-level

Last updated over 4 years ago

10 questions

In this lesson we are going to investigate absolute value equations in the graphing form of f(x) = a|x-h| + k, we will determine how numbers at a, h and k transform the parabola.  

The first thing we need to know is the shape of an absolute value function.  

Graph the parent function f(x) = |x| by using a table and evaluating f(-3), f(-2), f(-1), f(0), f(1), f(2), f(3).

We have released a new and improved Graphing question type! Students will no longer be able to answer this question.

What is the slope of the right half of the graph where x > 0?

What is the slope of the left half of the graph where x < 0?

We will call the point where the two halves meet (the point of the V shape), the vertex.
Given the equation f(x) = |x + 7| - 4. Where is the vertex of f(x)?

Check you answer above by graphing f(x) = |x + 7| - 4. The absolute value symbol of a vertical line "|" is on most keyboards, or you can use the keyboard button.

We have released a new and improved Graphing question type! Students will no longer be able to answer this question.

Now we need to determine how "a" transforms the graph of a absolute value equation.

Graph the function f(x) = 2|x|

We have released a new and improved Graphing question type! Students will no longer be able to answer this question.

Describe how an "a" value of 2 transforms the parent graph.

Graph f(x) = -3|x|

We have released a new and improved Graphing question type! Students will no longer be able to answer this question.

Describe how an "a" value of -3 transforms the parent graph.

Match the graph and its equation.

Draggable item		Corresponding Item
f(x) = 4\|x - 3\| - 1
f(x) = -2\|x - 3\| -1
f(x) = -\|x - 3\| -1

f(x)=3\|x - 3\| - 1

To further explore these transformations and how to write an exact equation given a graph.  Do the Desmos activity AA2-9 Graphing absolute values A-level.  The link is in the Canvas module.

Draggable item		Corresponding Item
f(x) = 4\|x - 3\| - 1
f(x) = -2\|x - 3\| -1
f(x) = -\|x - 3\| -1

f(x)=3\|x - 3\| - 1

Draggable item		Corresponding Item
f(x) = 4\|x - 3\| - 1
f(x) = -2\|x - 3\| -1
f(x) = -\|x - 3\| -1

f(x)=3\|x - 3\| - 1

AA2-9 graphing absolute value functions A-level

AA2-9 graphing absolute value functions A-level

Graph the parent function f(x) = |x| by using a table and evaluating f(-3), f(-2), f(-1), f(0), f(1), f(2), f(3).

What is the slope of the right half of the graph where x > 0?

What is the slope of the left half of the graph where x < 0?

We will call the point where the two halves meet (the point of the V shape), the vertex. Given the equation f(x) = |x + 7| - 4. Where is the vertex of f(x)?

Check you answer above by graphing f(x) = |x + 7| - 4. The absolute value symbol of a vertical line "|" is on most keyboards, or you can use the keyboard button.

Now we need to determine how "a" transforms the graph of a absolute value equation.Graph the function f(x) = 2|x|

Describe how an "a" value of 2 transforms the parent graph.

Graph f(x) = -3|x|

Describe how an "a" value of -3 transforms the parent graph.

Match the graph and its equation.

Graph the parent function f(x) = |x| by using a table and evaluating f(-3), f(-2), f(-1), f(0), f(1), f(2), f(3).

What is the slope of the right half of the graph where x > 0?

What is the slope of the left half of the graph where x < 0?

We will call the point where the two halves meet (the point of the V shape), the vertex. Given the equation f(x) = |x + 7| - 4. Where is the vertex of f(x)?

Check you answer above by graphing f(x) = |x + 7| - 4. The absolute value symbol of a vertical line "|" is on most keyboards, or you can use the keyboard button.

Now we need to determine how "a" transforms the graph of a absolute value equation.Graph the function f(x) = 2|x|

Describe how an "a" value of 2 transforms the parent graph.

Graph f(x) = -3|x|

Describe how an "a" value of -3 transforms the parent graph.

Match the graph and its equation.

We will call the point where the two halves meet (the point of the V shape), the vertex.
Given the equation f(x) = |x + 7| - 4. Where is the vertex of f(x)?

Now we need to determine how "a" transforms the graph of a absolute value equation.

Graph the function f(x) = 2|x|

We will call the point where the two halves meet (the point of the V shape), the vertex.
Given the equation f(x) = |x + 7| - 4. Where is the vertex of f(x)?

Now we need to determine how "a" transforms the graph of a absolute value equation.

Graph the function f(x) = 2|x|