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Absolute Value Functions
Algebra II Chapter 02 A BowerPoint Presentation
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The graph of y = |x|
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The graph of y = |x| When x is 3, what is y?
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The graph of y = |x| When x is 3, what is y? When x is -3, what is y?
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The graph of y = |x| When x is 3, what is y? When x is -3, what is y?
What point is the VERTEX of this function?
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The graph of y = |x| When x is 3, what is y? When x is -3, what is y?
What point is the VERTEX of this function? What is the slope of the right-side ray?
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Let’s make a table of points
The graph of y = 2|x – 1| + 3 Let’s make a table of points
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Let’s make a table of points
The graph of y = 2|x – 1| + 3 Let’s make a table of points X Y
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Let’s make a table of points
The graph of y = 2|x – 1| + 3 Let’s make a table of points X Y -1 1 2 3 Find the corresponding y values
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Let’s make a table of points
The graph of y = 2|x – 1| + 3 Let’s make a table of points X Y -1 1 2 3 7 5 3 Do you notice anything?
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Let’s make a graph using those points
The graph of y = 2|x – 1| + 3 Let’s make a graph using those points
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The graph of y = 2|x – 1| + 3
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The graph of y = 2|x – 1| + 3 What is the VERTEX of this graph?
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The graph of y = 2|x – 1| + 3 What is the VERTEX of this graph?
What is the slope of the right-side ray?
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The graph of y = 2|x – 1| + 3 What is the VERTEX of this graph?
What is the slope of the right-side ray? Does this graph open UP or DOWN?
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The graph of y = 2|x – 1| + 3 What is the VERTEX of this graph?
What is the slope of the right-side ray? Does this graph open UP or DOWN? Is this graph WIDER, NARROWER, or THE SAME as the graph of y = |x|?
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What’s up w/absolute value functions
y = a | x – h | + k Do you see how this looks like y – y1 = m (x – x1) ? [Maybe not yet – let’s move y1…]
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What’s up w/absolute value functions
y = a | x – h | + k Do you see how this looks like y – y1 = m (x – x1) ?
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What’s up w/absolute value functions
y = a | x – h | + k Do you see how this looks like y= m (x – x1) + y1 ?
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What’s up w/absolute value functions
y = a | x – h | + k Do you see how this looks like y= m (x – x1) + y1 ?
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What’s up w/absolute value functions
y = a | x – h | + k The vertex of this graph will be the point (h, k)
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What’s up w/absolute value functions
y = a | x – h | + k The slope of the right-side ray will be a
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What’s up w/absolute value functions
y = a | x – h | + k The slope of the right-side ray will be a The slope of the left-side ray will be -a
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What’s up w/absolute value functions
y = a | x – h | + k If a is POSITIVE If a is NEGATIVE Graph opens Graph opens UP DOWN
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What’s up w/absolute value functions
y = a | x – h | + k If |a| > 1 If |a| = 1 If |a| < 1 Narrower Same width Wider than y =|x| than y =|x| than y =|x|
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Graph this absolute value function: y = – |x + 2| – 3
Let’s graph! Graph this absolute value function: y = – |x + 2| – 3
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Graph this absolute value function: y = – |x + 2| – 3
Let’s graph! Graph this absolute value function: y = – |x + 2| – 3 Will this graph open UP or DOWN?
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Graph this absolute value function: y = – |x + 2| – 3
Let’s graph! Graph this absolute value function: y = – |x + 2| – 3 Will this graph open UP or DOWN? What will be the VERTEX of this graph?
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Graph this absolute value function: y = – |x + 2| – 3
Let’s graph! Graph this absolute value function: y = – |x + 2| – 3 Will this graph open UP or DOWN? What will be the VERTEX of this graph? What is the slope of the right-side ray?
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Graph this absolute value function: y = – |x + 2| – 3
Let’s graph! Graph this absolute value function: y = – |x + 2| – 3 Will this graph open UP or DOWN? What will be the VERTEX of this graph? What is the slope of the right-side ray? Use symmetry to draw the left-side ray.
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Graph this absolute value function: y = – |x + 2| – 3
Let’s graph! Graph this absolute value function: y = – |x + 2| – 3 Will this graph open UP or DOWN? What will be the VERTEX of this graph? What is the slope of the right-side ray? Use symmetry to draw the left-side ray. Is this NARROWER, WIDER, or THE SAME as y = |x| ?
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Let’s graph!
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Graph this absolute value function: y = 2/3 |x – 4| + 2
Let’s graph again! Graph this absolute value function: y = 2/3 |x – 4| + 2
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Graph this absolute value function: y = 2/3 |x – 4| + 2
Let’s graph again! Graph this absolute value function: y = 2/3 |x – 4| + 2 Will this graph open UP or DOWN?
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Graph this absolute value function: y = 2/3 |x – 4| + 2
Let’s graph! Graph this absolute value function: y = 2/3 |x – 4| + 2 Will this graph open UP or DOWN? What will be the VERTEX of this graph?
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Graph this absolute value function: y = 2/3 |x – 4| + 2
Let’s graph again! Graph this absolute value function: y = 2/3 |x – 4| + 2 Will this graph open UP or DOWN? What will be the VERTEX of this graph? What is the slope of the right-side ray?
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Graph this absolute value function: y = 2/3 |x – 4| + 2
Let’s graph again! Graph this absolute value function: y = 2/3 |x – 4| + 2 Will this graph open UP or DOWN? What will be the VERTEX of this graph? What is the slope of the right-side ray? Use symmetry to draw the left-side ray.
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Graph this absolute value function: y = 2/3 |x – 4| + 2
Let’s graph again! Graph this absolute value function: y = 2/3 |x – 4| + 2 Will this graph open UP or DOWN? What will be the VERTEX of this graph? What is the slope of the right-side ray? Use symmetry to draw the left-side ray. Is this NARROWER, WIDER, or THE SAME as y = |x| ?
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Let’s graph again!
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Turning graph into a function
We will follow these steps to turn a graph into an absolute value function… Find the vertex – this gives us h and k. Find the slope of the right side ray – this gives us a. Put our h, k, and a into y = a | x – h | + k
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Turning graph into a function
Let’s turn the following graph into a function!
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Turning graph into a function
Step 1- Find the vertex (to get h & k)
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Turning graph into a function
Step 1- Find the vertex (to get h & k) What is the vertex?
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Turning graph into a function
Step 1- Find the vertex (to get h & k) What is the vertex? (– 4, –1)
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Turning graph into a function
Step 1- Find the vertex (to get h & k) What is the vertex? (– 4, –1) h = –4 & k = –1
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Turning graph into a function
Step 2- Find the slope of the right-side ray (to get a)
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Turning graph into a function
Step 2- Find the slope of the right-side ray (to get a) What is the slope (go from vertex to P1)?
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Turning graph into a function
Step 2- Find the slope of the right-side ray (to get a) What is the slope (go from vertex to P1)? Slope is –3/2 , so a = –3/2.
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Turning graph into a function
Step 3- Put our h, k, and a into y = a | x – h | + k
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Turning graph into a function
Step 3- Put our h, k, and a into y = a | x – h | + k a = –3/2 h = –4 k = –1
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Turning graph into a function
Step 3- Put our h, k, and a into y = a | x – h | + k a = –3/2 h = –4 k = –1
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Turning graph into a function
Step 3- y = –3/2 | x – (–4) | + –1 Let’s make this look neater!
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Turning graph into a function
Step 3- y = –3/2 | x + 4 | – 1 We’re done!
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